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Class 11 • Physics
Work, Energy and Power & Circular Motion
Chapter-5
359 Questions
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74 Easy271 Medium14 Hard
Practice Questions
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Showing 359 of 359 questions
1
MediumJEE Mains2026
A body of mass 1 kg moves along a straight line with a velocity v=2 x^2. The work done by the body during displacement from x=0 to 5 m is \_\_\_\_ J.
Options:
A) 0
B) 250
C) 1250
D) 1000
2
MediumAiims2019
An electron is moving in a circle of radius 2m with speed of 4 m/s. Find the acceleration of the electron.
Options:
A) 8 m/s$^2
B) 4 m/s$^2
C) 16 m/s$^2
D) 10 m/s$^2
3
MediumJEE Mains2026
The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is \_\_\_\_ \mathrm{m} / \mathrm{s}. Assume pulley is massless and string is light and inextensible. (Take \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )
Options:
A) 7.74
B) 7.20
C) 6.55
D) 4.50
4
MediumAiims2017
The particle of mass $m is moving in a circular path of constant radius r such that its centripetal acceleration a_c is varying with time t as a_c=k^2 r t^2, where k$ is a constant. The power delivered to particle by the forces acting on it is
Options:
A) 2 \pi m k^2 r^2 t
B) m k^2 r^2 t
C) 1 / 3 m k^4 r^2 t^5
D) zero
5
HardJEE Mains2026
The rain drop of mass 1 g , starts with zero velocity from a height of 1 km . It hits the ground with a speed of 5 \mathrm{~m} / \mathrm{s}. The work done by the unknown resistive force is \_\_\_\_ J. (take \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )
Options:
A) -8.75
B) -8.35
C) -9.55
D) -9.98
6
MediumAiims2017
Assertion : For looping a vertical loop of radius, $r the minimum velocity at lowest point should be \sqrt{5 g r}$. Reason : In this event the velocity at the highest point will be zero.
Options:
A) Both assertion and reason are true and reason is the correct explanation of assertion
B) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false
D) Both assertion and reason are false.
7
HardJEE Mains2026
A mass of 1 kg is kept on a inclined plane with 30^{\circ} inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of 4 \mathrm{~m} / \mathrm{s}. The work done by the frictional force in time 2 s is \_\_\_\_ J. (Take g=10 \mathrm{~m} / \mathrm{s}^2 )
Options:
A) 20
B) 25
C) 30
D) 10
8
MediumBITSAT2021
A cyclist speeding at 6 m/s in a circle of 18 m radius makes an angle $\theta$ with the vertical. The minimum possible value of coefficient of friction between the tyres and the ground is
Options:
A) 12.041
B) 0.2041
C) 11.32
D) 10.020
9
HardJEE Mains2026
A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is _________ N. (Take g = 10 \ \mathrm{m/s^2})
Options:
A) 1980
B) 2020
C) 2000
D) 1000
10
MediumCOMEDK2025
A point marked on a ring of radius 2 cm is in contact with a horizontal plane. Now the ring is rolled forward half a revolution along the positive X - direction. Then the angle made by the displacement vector of the point with the X - axis is:
Options:
A) \theta=\boldsymbol{\operatorname { t a n }}^{-\mathbf{1}}\left(\frac{\mathbf{2}}{\mathbf{3} \boldsymbol{\pi}}\right)
B) \boldsymbol{\theta}=\boldsymbol{\operatorname { t a n }}^{-\mathbf{1}}\left(\frac{\mathbf{2}}{\boldsymbol{\pi}}\right)
C) \theta=\tan ^{-1}\left(\frac{2 \pi}{3}\right)
D) \theta=\cot ^{-1}\left(\frac{2}{\pi}\right)
11
HardJEE Mains2026
A bead P sliding on a frictionless semi-circular string (A C B) and it is at point S at t =0 and at this instant the horizontal component of its velocity is v. Another bead Q of the same mass as P is ejected from point A at t=0 along the horizontal string A B, with the speed v, friction between the beads and the respective strings may be neglected in both cases. Let t_P and t_Q be the respective times taken by beads P and Q to reach the point B, then the relation between t_P and t_Q is
Options:
A) t_P < t_Q
B) t_P=t_Q
C) t_P>1.25 t_Q
D) t_P>t_Q
12
MediumCOMEDK2025
A coin is placed on a disc rotating with an angular velocity \omega. The co-efficient of friction between the disc and the coin is \mu. The maximum distance of the coin from the centre of the disc up to which it will rotate with the disc is
Options:
A) \sqrt{\frac{\mu}{\omega^2}}
B) \frac{\mu g}{\omega^2}
C) \sqrt{\frac{\mu g}{\omega^2}}
D) \frac{\mu g}{\omega}
13
MediumJEE Mains2026
An object is projected with kinetic energy K from a point A at an angle 60^{\circ} with the horizontal. The ratio of the difference in kinetic energies at points B and C to that at point A (see figure), in the absence of air friction is :
Options:
A) 3: 4
B) 1: 4
C) 2: 3
D) 1: 2
14
MediumCOMEDK2024
A ball is moving in a circular path of radius $5 \mathrm{~m}. If tangential acceleration at any instant is 10 \mathrm{~ms}^{-2} and the net acceleration makes an angle of 30^{\circ}$ with the centripetal acceleration, then, the instantaneous speed is
Options:
A) 5.4 \mathrm{~ms}^{-1}
B) 50 \sqrt{3} \mathrm{~ms}^{-1}
C) 6.6 \mathrm{~ms}^{-1}
D) 9.3 \mathrm{~ms}^{-1}
15
MediumJEE Mains2026
Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E. The energy stored in B, when spring constants k_A, k_B of A and B, respectively satisfy the relation 4 k_A=3 k_B, is :
Options:
A) 4 E
B) 2 E
C) \frac{4}{3} E
D) 3 E
16
MediumCOMEDK2024
A metal ball of $20 \mathrm{~g} is projected at an angle 30^{\circ} with the horizontal with an initial velocity 10 \mathrm{~ms}^{-1}$. If the mass and angle of projection are doubled keeping the initial velocity the same, the ratio of the maximum height attained in the former to the latter case is :
Options:
A) 1 : 2
B) 2 : 1
C) 1 : 3
D) 3 : 1
17
EasyJEE Mains2026
Given below are two statements : Statement I : An object moves from position r_1 to position r_2 under a conservative force field \vec{F}. The work done by the force is W=-\int\limits_{r_1}^{r_2} \vec{F} \cdot \overrightarrow{d r}. Statement II : Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force. In the light of the above statements, choose the correct answer from the options given below :
Options:
A) Statement I is true but Statement II is false
B) Statement I is false but Statement II is true
C) Both Statement I and Statement II are false
D) Both Statement I and Statement II are true
18
MediumCOMEDK2024
A body is moving along a circular path of radius '$r' with a frequency of revolution numerically equal to the radius of the circular path. What is the acceleration of the body if radius of the path is \left(\frac{5}{\pi}\right) m$ ?
Options:
A)
100 \pi \mathrm{~ms}^{-2}
B)
500 \pi \mathrm{~ms}^{-2}
C)
25 \pi \mathrm{~ms}^{-2}
D)
\left(\frac{500}{\pi}\right) \mathrm{ms}^{-2}
19
EasyJEE Mains2026
A body of mass 2 kg is moving along x -direction such that its displacement as function of time is given by x(t) = \alpha t^2 + \beta t + \gamma m, where \alpha = 1 \; m/s^2, \beta = 1 \; m/s and \gamma = 1 \; m. The work done on the body during the time interval t = 2 \; s to t = 3 \; s, is ________ J.
Options:
A) 42
B) 24
C) 49
D) 12
20
MediumCOMEDK2023
One end of the string of length l is connected to a particle of mass $m and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed v, the net force on the particle (directed towards centre) will be ( T$ represents the tension in the string)
Options:
A) T
B) T+\frac{m v^2}{l}
C) T-\frac{m v^2}{l}
D) zero
21
MediumJEE Mains2026
Potential energy ( V ) versus distance ( x ) is given by the graph. Rank various regions as per the magnitudes of the force ( F ) acting on a particle from high to low.
Options:
A) F_{B C}>F_{A B}>F_{D E}>F_{C D}
B) F_{B C}>F_{C D}>F_{D E}>F_{A B}
C) F_{C D}>F_{A B}>F_{B C}>F_{D E}
D) F_{C D}>F_{D E}>F_{A B}>F_{B C}
22
MediumCOMEDK2021
When a car of mass $m is moving with speed v along a circle of radius r on a level road, the centripetal force is provided by f, where f denotes (\mu_s \to coefficient of friction, N \to$ normal reaction)
Options:
A) {{m{v^2}} \over r} = f \le {\mu _s}N
B) f < {\mu _s} = {{m{v^2}} \over r}
C) f = {\mu _s}N = {{m{v^2}} \over r}
D) f = {\mu _k}N = {{m{v^2}} \over r}
23
EasyJEE Mains2025
Which one of the following forces cannot be expressed in terms of potential energy?
Options:
A) Frictional force
B) Coulomb’s force
C) Restoring force
D) Gravitational force
24
MediumJEE Mains2026
A car moving with a speed of 54 \mathrm{~km} / \mathrm{h} takes a turn of radius 20 m . A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take g=10 \mathrm{~m} / \mathrm{s}^2 )
Options:
A) \tan ^{-1}(0.5)
B) \tan ^{-1}(0.75)
C) \tan ^{-1}(1.125)
D) \tan ^{-1}(0.25)
25
MediumJEE Mains2025
An object of mass 1000 g experiences a time dependent force \vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) N. The power generated by the force at time t is:
Options:
A) \left(2 t^2+18 t^3\right) W
B) \left(3 t^3+5 t^5\right) w
C) \left(2 t^3+3 t^5\right) w
D) \left(2 t^2+3 t^3\right) w
26
MediumJEE Mains2026
A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height h as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height h=\alpha R. The value of \alpha is \_\_\_\_
Options:
A) 2
B) 4
C) 3
D) 6
27
MediumJEE Mains2025
A block of mass 25 kg is pulled along a horizontal surface by a force at an angle 45^{\circ} with the horizontal. The friction coefficient between the block and the surface is 0.25 . The block travels at a uniform velocity. The work done by the applied force during a displacement of 5 m of the block is :
Options:
A) 490 J
B) 970 J
C) 735 J
D) 245 J
28
MediumJEE Mains2026
A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is 5 rad/s. The coefficient of friction between the drum’s inner wall surface and mass is _________. (Take g = 10\ \mathrm{m/s^2})
Options:
A) 0.1
B) 0.5
C) 0.7
D) 0.3
29
EasyJEE Mains2025
A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.
Options:
A) \frac{\mathrm{S}}{4}, \frac{3 \mathrm{gS}}{2}
B) \frac{\mathrm{S}}{2}, \frac{3 \mathrm{gS}}{2}
C) \frac{\mathrm{S}}{4}, \sqrt{\frac{3 \mathrm{gS}}{2}}
D) \frac{\mathrm{S}}{2}, \sqrt{\frac{3 \mathrm{gS}}{2}}
30
MediumJEE Mains2026
A particle is rotating in a circular path and at any instant its motion can be described as \theta = \frac{5t^4}{40} - \frac{t^3}{3}. The angular acceleration of the particle after 10 seconds is _________ rad/s 2 .
Options:
A) 150
B) 120
C) 130
D) 170
31
MediumJEE Mains2025
A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e., \frac{dm}{dt} \propto \sqrt{v}. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?
Options:
A) P \propto \sqrt{v}
B) P \propto v
C) P^2 \propto v^3
D) P^2 \propto v^5
32
MediumJEE Mains2026
In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle 30^{\circ} shown in figure, the velocity at the bottom point (A) of the circular path is (g = gravitational acceleration)
Options:
A) \sqrt{\frac{7}{2} g r}
B) \sqrt{4 g r}
C) \sqrt{\frac{5}{2} g r}
D) \sqrt{5 g r}
33
MediumJEE Mains2025
A body of mass 4 kg is placed on a plane at a point P having coordinate (3,4) \mathrm{m}. Under the action of force \overrightarrow{\mathrm{F}}=(2 \hat{i}+3 \hat{j}) \mathrm{N}, it moves to a new point Q having coordinates (6,10) \mathrm{m} in 4 sec . The average power and instanteous power at the end of 4 sec are in the ratio of :
Options:
A) 4 : 3
B) 13 : 6
C) 1 : 2
D) 6 : 13
34
MediumJEE Mains2026
A large drum having radius R is spinning around its axis with angular velocity \omega, as shown in figure. The minimum value of \omega so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M as \mu, is :
Options:
A) \sqrt{\dfrac{2g}{\mu R}}
B) \sqrt{\dfrac{g}{2\mu R}}
C) \sqrt{\dfrac{\mu g}{R}}
D) \sqrt{\dfrac{g}{\mu R}}
35
MediumJEE Mains2025
A bead of mass ' m ' slides without friction on the wall of a vertical circular hoop of radius ' R ' as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is ' R '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity)
Options:
A) \sqrt{2 R g+\frac{\mathrm{kR}^2}{\mathrm{~m}}}
B) \sqrt{3 \mathrm{Rg}+\frac{\mathrm{kR}^2}{\mathrm{~m}}}
C) \sqrt{2 \mathrm{Rg}+\frac{4 \mathrm{kR}^2}{\mathrm{~m}}}
D) 2\sqrt{\mathrm{gR}+\frac{\mathrm{kR}^2}{\mathrm{~m}}}
36
EasyJEE Mains2026
Two cars A and B each of mass 10^3 kg are moving on parallel tracks separated by a distance of 10 m, in same direction with speeds 72 km/h and 36 km/h. The magnitude of angular momentum of car A with respect to car B is ________ J·s.
Options:
A) 3.6 \times 10^{5}
B) 10^{5}
C) 3 \times 10^{5}
D) 2 \times 10^{5}
37
MediumJEE Mains2025
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason \mathbf{R} Assertion A: In a central force field, the work done is independent of the path chosen. Reason R: Every force encountered in mechanics does not have an associated potential energy. In the light of the above statements, choose the most appropriate answer from the options given below
Options:
A) \mathbf{A} is false but \mathbf{R} is true
B) Both \mathbf{A} and \mathbf{R} are true but \mathbf{R} is NOT the correct explanation of \mathbf{A}
C) \mathbf{A} is true but \mathbf{R} is false
D) Both \mathbf{A} and \mathbf{R} are true and \mathbf{R} is the correct explanation of \mathbf{A}
38
MediumJEE Mains2025
A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is 8 \mathrm{~m} / \mathrm{s}. The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be :
Options:
A) 4 \sqrt{2} \mathrm{~m} / \mathrm{s}
B) 8 \mathrm{~m} / \mathrm{s}
C) 4 \mathrm{~m} / \mathrm{s}
D) 8 \sqrt{2} \mathrm{~m} / \mathrm{s}
39
EasyJEE Mains2025
A force \mathrm{F}=\alpha+\beta \mathrm{x}^2 acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant \alpha=1 \mathrm{~N} then \beta will be
Options:
A) 15 \mathrm{~N} / \mathrm{m}^2
B) 10 \mathrm{~N} / \mathrm{m}^2
C) 12 \mathrm{~N} / \mathrm{m}^2
D) 8 \mathrm{~N} / \mathrm{m}^2
40
EasyJEE Mains2025
A sportsman runs around a circular track of radius r such that he traverses the path A B A B. The distance travelled and displacement, respectively, are
Options:
A) \pi r, 3 r
B) 2 \mathrm{r}, 3 \pi \mathrm{r}
C) 3 \pi \mathrm{r}, 2 \mathrm{r}
D) 3 \pi r, \pi r
41
EasyJEE Mains2025
A ball having kinetic energy KE, is projected at an angle of 60^{\circ} from the horizontal. What will be the kinetic energy of ball at the highest point of its flight?
Options:
A) \frac{(\mathrm{KE})}{2}
B) \frac{(\mathrm{KE})}{8}
C) \frac{(\mathrm{KE})}{4}
D) \frac{(\mathrm{KE})}{16}
42
MediumJEE Mains2025
A body of mass ‘m’ connected to a massless and unstretchable string goes in vertical circle of radius ‘R’ under gravity g. The other end of the string is fixed at the center of circle. If velocity at top of circular path is n\sqrt{ g R} , where, n ≥ 1, then ratio of kinetic energy of the body at bottom to that at top of the circle is :
Options:
A) \frac{n^2 + 4}{n^2}
B) \frac{n + 4}{n}
C) \frac{n^2}{n^2 + 4}
D) \frac{n}{n + 4}
43
EasyJEE Mains2025
A force \overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k} is applied on a particle and it undergoes a displacement \hat{i}-2 \hat{j}-\hat{k} What will be the value of b, if work done on the particle is zero.
Options:
A) \frac{1}{3}
B) \frac{1}{2}
C) 0
D) 2
44
MediumJEE Mains2025
A car of mass ' m ' moves on a banked road having radius ' r ' and banking angle \theta. To avoid slipping from banked road, the maximum permissible speed of the car is v_0. The coefficient of friction \mu between the wheels of the car and the banked road is
Options:
A) \mu=\frac{v_0^2+r g \tan \theta}{r g+v_0^2 \tan \theta}
B) \mu=\frac{v_0^2-r g \tan \theta}{\mathrm{rg}-\mathrm{v}_{\mathrm{o}}^2 \tan \theta}
C) \mu=\frac{v_0^2-r g \tan \theta}{r g+v_0^2 \tan \theta}
D) \mu=\frac{v_o^2+r g \tan \theta}{r g-v_o^2 \tan \theta}
45
EasyJEE Mains2024
A particle of mass $m moves on a straight line with its velocity increasing with distance according to the equation v=\alpha \sqrt{x}, where \alpha is a constant. The total work done by all the forces applied on the particle during its displacement from x=0 to x=\mathrm{d}$, will be :
Options:
A) \frac{\mathrm{m}}{2 \alpha^2 \mathrm{~d}}
B) \frac{\mathrm{md}}{2 \alpha^2}
C) \frac{\mathrm{m} \alpha^2 \mathrm{~d}}{2}
D) 2 \mathrm{~m} \alpha^2 \mathrm{~d}
46
MediumJEE Mains2025
A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 \mathrm{~m} / \mathrm{s}. The ratio of its kinetic energies at point B and C is : (Take acceleration due to gravity as 10 \mathrm{~m} / \mathrm{s}^2)
Options:
A) \frac{3-\sqrt{2}}{2}
B) \frac{2+\sqrt{3}}{3}
C) \frac{2+\sqrt{2}}{3}
D) \frac{3+\sqrt{3}}{2}
47
MediumJEE Mains2024
A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :
Options:
A) \sqrt{6} \mathrm{~m}
B) \sqrt{5} \mathrm{~m}
C) 1 \mathrm{~m}
D) 2 \mathrm{~m}
48
MediumJEE Mains2025
A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity v_0 at the point ' A ', the string becomes slack when, the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points B and C is _________.
Options:
A) 4
B) 1
C) 2
D) 3
49
EasyJEE Mains2024
Three bodies A, B and C have equal kinetic energies and their masses are $400 \mathrm{~g}, 1.2 \mathrm{~kg} and 1.6 \mathrm{~kg}$ respectively. The ratio of their linear momenta is :
Options:
A) 1: \sqrt{3}: 2
B) \sqrt{3}: \sqrt{2}: 1
C) 1: \sqrt{3}: \sqrt{2}
D) \sqrt{2} : \sqrt{3}: 1
50
MediumJEE Mains2024
A clock has $75 \mathrm{~cm}, 60 \mathrm{~cm} long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take \pi=3.14$) :
Options:
A) 118.9
B) 140.5
C) 139.4
D) 220.0
51
EasyJEE Mains2024
When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :
Options:
A) 60%
B) 500%
C) 6%
D) 600%
52
MediumJEE Mains2024
A car of $800 \mathrm{~kg} is taking turn on a banked road of radius 300 \mathrm{~m} and angle of banking 30^{\circ}. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: (\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73)
Options:
A) 51.4 m/s
B) 102.8 m/s
C) 70.4 m/s
D) 264 m/s
53
EasyJEE Mains2024
A bullet of mass $50 \mathrm{~g} is fired with a speed 100 \mathrm{~m} / \mathrm{s} on a plywood and emerges with 40 \mathrm{~m} / \mathrm{s}$. The percentage loss of kinetic energy is :
Options:
A) 44 \%
B) 16 \%
C) 84 \%
D) 32 \%
54
EasyJEE Mains2024
A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $9 \mathrm{~m} and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in \mathrm{m} / \mathrm{s}^2$ ) :
Options:
A) 4 \pi^2 \mathrm{~ms}^{-2}
B) 16 \pi^2 \mathrm{~ms}^{-2}
C) 57600 \pi^2 \mathrm{~ms}^{-2}
D) Zero
55
EasyJEE Mains2024
Four particles $A, B, C, D of mass \frac{m}{2}, m, 2 m, 4 m$, have same momentum, respectively. The particle with maximum kinetic energy is :
Options:
A) B
B) C
C) D
D) A
56
EasyJEE Mains2024
A cyclist starts from the point $P of a circular ground of radius 2 \mathrm{~km} and travels along its circumference to the point \mathrm{S}$. The displacement of a cyclist is:
Options:
A) \sqrt8$ km
B) 4 km
C) 6 km
D) 8 km
57
MediumJEE Mains2024
A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :
Options:
A) t
2/3
B) t
3/2
C) t
D) t
2
58
EasyJEE Mains2024
A ball of mass 0.5 \mathrm{~kg} is attached to a string of length 50 \mathrm{~cm}. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400 \mathrm{~N}. The maximum possible value of angular velocity of the ball in \mathrm{rad} / \mathrm{s} is, :
Options:
A) 1600
B) 20
C) 40
D) 1000
59
EasyJEE Mains2024
A body of mass $50 \mathrm{~kg} is lifted to a height of 20 \mathrm{~m}$ from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be :
Options:
A) 2: 1
B) \sqrt{3}: 2
C) 1: 1
D) 1: 2
60
MediumJEE Mains2024
A particle moving in a circle of radius \mathrm{R} with uniform speed takes time \mathrm{T} to complete one revolution. If this particle is projected with the same speed at an angle \theta to the horizontal, the maximum height attained by it is equal to 4 R. The angle of projection \theta is then given by :
Options:
A) \sin ^{-1}\left[\frac{2 \mathrm{gT}^2}{\pi^2 \mathrm{R}}\right]^{\frac{1}{2}}
B) \sin ^{-1}\left[\frac{\pi^2 \mathrm{R}}{2 \mathrm{gT}^2}\right]^{\frac{1}{2}}
C) \cos ^{-1}\left[\frac{\pi \mathrm{R}}{2 \mathrm{gT}^2}\right]^{\frac{1}{2}}
D) \cos ^{-1}\left[\frac{2 \mathrm{gT}^2}{\pi^2 \mathrm{R}}\right]^{\frac{1}{2}}
61
MediumJEE Mains2024
A body of $m \mathrm{~kg} slides from rest along the curve of vertical circle from point A to B in friction less path. The velocity of the body at B is: (given, R=14 \mathrm{~m}, g=10 \mathrm{~m} / \mathrm{s}^2 and \sqrt{2}=1.4$)
Options:
A) 10.6 m/s
B) 19.8 m/s
C) 16.7 m/s
D) 21.9 m/s
62
EasyJEE Mains2024
A coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu. If the distance of the coin from the center of the disc is r$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :
Options:
A) \sqrt{\frac{r}{\mu g}}
B) \sqrt{\frac{\mu g}{r}}
C) \frac{\mu g}{r}
D) \frac{\mu}{\sqrt{r g}}
63
EasyJEE Mains2024
If a rubber ball falls from a height $h and rebounds upto the height of h / 2$. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :
Options:
A) 50 \%, \sqrt{2 \mathrm{gh}}
B) 50 \%, \sqrt{\mathrm{gh}}
C) 50 \%, \sqrt{\frac{\text { gh }}{2}}
D) 40 \%, \sqrt{2 \mathrm{gh}}
64
MediumJEE Mains2024
A stone of mass $900 \mathrm{~g} is tied to a string and moved in a vertical circle of radius 1 \mathrm{~m} making 10 \mathrm{~rpm}. The tension in the string, when the stone is at the lowest point is (if \pi^2=9.8 and g=9.8 \mathrm{~m} / \mathrm{s}^2$) :
Options:
A) 17.8 N
B) 97 N
C) 9.8 N
D) 8.82 N
65
MediumJEE Mains2024
A body of mass $2 \mathrm{~kg} begins to move under the action of a time dependent force given by \vec{F}=\left(6 t \hat{i}+6 t^2 \hat{j}\right) N. The power developed by the force at the time t$ is given by:
Options:
A) \left(3 t^3+6 t^5\right) W
B) \left(9 t^5+6 t^3\right) W
C) \left(6 t^4+9 t^5\right) W
D) \left(9 t^3+6 t^5\right) W
66
EasyJEE Mains2024
If the radius of curvature of the path of two particles of same mass are in the ratio $3: 4$, then in order to have constant centripetal force, their velocities will be in the ratio of :
Options:
A) 1: \sqrt{3}
B) 2: \sqrt{3}
C) \sqrt{3}: 2
D) \sqrt{3}: 1
67
MediumJEE Mains2024
A block of mass $1 \mathrm{~kg} is pushed up a surface inclined to horizontal at an angle of 60^{\circ} by a force of 10 \mathrm{~N} parallel to the inclined surface as shown in figure. When the block is pushed up by 10 \mathrm{~m} along inclined surface, the work done against frictional force is : \left[g=10 \mathrm{~m} / \mathrm{s}^2\right]
Options:
A) 5$\sqrt3$ J
B) 5 J
C) 5\times10^3$ J
D) 10 J
68
EasyJEE Mains2024
A train is moving with a speed of $12 \mathrm{~m} / \mathrm{s} on rails which are 1.5 \mathrm{~m} apart. To negotiate a curve radius 400 \mathrm{~m}, the height by which the outer rail should be raised with respect to the inner rail is (Given, g=10 \mathrm{~m} / \mathrm{s}^2)$ :
Options:
A) 6.0 cm
B) 5.4 cm
C) 4.8 cm
D) 4.2 cm
69
EasyJEE Mains2024
A particle is placed at the point $A of a frictionless track A B C as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is : (Take g=10 \mathrm{~m} / \mathrm{s}^2$).
Options:
A) 2 \sqrt{10} \mathrm{~m} / \mathrm{s}
B) 10 \mathrm{~m} / \mathrm{s}
C) \sqrt{10} \mathrm{~m} / \mathrm{s}
D) 20 \mathrm{~m} / \mathrm{s}
70
EasyJEE Mains2023
A vehicle of mass $200 \mathrm{~kg} is moving along a levelled curved road of radius 70 \mathrm{~m} with angular velocity of 0.2 ~\mathrm{rad} / \mathrm{s}$. The centripetal force acting on the vehicle is:
Options:
A) 560 \mathrm{~N}
B) 14 \mathrm{~N}
C) 2800 \mathrm{~N}
D) 2240 \mathrm{~N}
71
MediumJEE Mains2024
A bob of mass '$m' is suspended by a light string of length 'L'. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies \frac{(K . E)_A}{(K . E)_B}$ is :
Options:
A) 5 : 1
B) 3 : 2
C) 1 : 5
D) 2 : 5
72
EasyJEE Mains2023
A coin placed on a rotating table just slips when it is placed at a distance of $1 \mathrm{~cm}$ from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of _________ from the centre :
Options:
A) 1 cm
B) 8 cm
C) 4 cm
D) 2 cm
73
EasyJEE Mains2024
A block of mass $100 \mathrm{~kg} slides over a distance of 10 \mathrm{~m} on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction (\operatorname{in} J$) is :
Options:
A) 3900
B) 4500
C) 4200
D) 4000
74
MediumJEE Mains2023
As shown in the figure, a particle is moving with constant speed $\pi ~\mathrm{m} / \mathrm{s}. Considering its motion from \mathrm{A} to \mathrm{B}$, the magnitude of the average velocity is :
Options:
A) \pi ~\mathrm{m} / \mathrm{s}
B) 1.5 \sqrt{3} \mathrm{~m} / \mathrm{s}
C) \sqrt{3} \mathrm{~m} / \mathrm{s}
D) 2 \sqrt{3} \mathrm{~m} / \mathrm{s}
75
EasyJEE Mains2024
The potential energy function (in $J ) of a particle in a region of space is given as U=\left(2 x^2+3 y^3+2 z\right). Here x, y and z are in meter. The magnitude of x-component of force (in N ) acting on the particle at point P(1,2,3) \mathrm{m}$ is :
Options:
A) 4
B) 2
C) 8
D) 6
76
EasyJEE Mains2023
A child of mass $5 \mathrm{~kg} is going round a merry-go-round that makes 1 rotation in 3.14 \mathrm{~s}. The radius of the merry-go-round is 2 \mathrm{~m}$. The centrifugal force on the child will be
Options:
A) 50 N
B) 80 N
C) 100 N
D) 40 N
77
MediumJEE Mains2024
A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $(\theta)$ of thread deflection in the extreme position will be :
Options:
A) \tan ^{-1}\left(\frac{1}{2}\right)
B) 2 \tan ^{-1}\left(\frac{1}{2}\right)
C) 2 \tan ^{-1}\left(\frac{1}{\sqrt{5}}\right)
D) \tan ^{-1}(\sqrt{2})
78
MediumJEE Mains2023
A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ}, the ratio of instantaneous velocity to its average velocity is \pi: x \sqrt{2}. The value of x$ will be -
Options:
A) 1
B) 7
C) 5
D) 2
79
MediumJEE Mains2024
A bullet is fired into a fixed target looses one third of its velocity after travelling $4 \mathrm{~cm}. It penetrates further \mathrm{D} \times 10^{-3} \mathrm{~m} before coming to rest. The value of \mathrm{D}$ is :
Options:
A) 23
B) 32
C) 42
D) 52
80
MediumJEE Mains2023
A small block of mass $100 \mathrm{~g} is tied to a spring of spring constant 7.5 \mathrm{~N} / \mathrm{m} and length 20 \mathrm{~cm}. The other end of spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity 5 ~\mathrm{rad} / \mathrm{s} about point \mathrm{A}$, then tension in the spring is -
Options:
A) 0.50 N
B) 1.5 N
C) 0.75 N
D) 0.25 N
81
MediumJEE Mains2023
The ratio of powers of two motors is $\frac{3 \sqrt{x}}{\sqrt{x}+1}, that are capable of raising 300 \mathrm{~kg} water in 5 minutes and 50 \mathrm{~kg} water in 2 minutes respectively from a well of 100 \mathrm{~m} deep. The value of x$ will be
Options:
A) 16
B) 4
C) 2
D) 2.4
82
MediumJEE Mains2023
A stone of mass 1 \mathrm{~kg} is tied to end of a massless string of length 1 \mathrm{~m}. If the breaking tension of the string is 400 \mathrm{~N}, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is :
Options:
A) 20 \mathrm{~ms}^{-1}
B) 40 \mathrm{~ms}^{-1}
C) 400 \mathrm{~ms}^{-1}
D) 10 \mathrm{~ms}^{-1}
83
EasyJEE Mains2023
Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is :
Options:
A) 3: 4
B) 4: 3
C) 9: 16
D) 16: 9
84
EasyJEE Mains2023
A body is moving with constant speed, in a circle of radius 10 \mathrm{~m}. The body completes one revolution in 4 \mathrm{~s}. At the end of 3rd second, the displacement of body (in \mathrm{m} ) from its starting point is :
Options:
A) 15 \pi
B) 30
C) 10 \sqrt{2}
D) 5 \pi
85
EasyJEE Mains2023
Given below are two statements: Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance. Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of given statements, choose the most appropriate answer from the options given below
Options:
A) Statement I is incorrect but Statement II is correct.
B) Statement $\mathrm{I}$ is correct but Statement II is incorrect.
C) Both Statement I and Statement II are correct.
D) Both Statement I and Statement II are incorrect.
86
EasyJEE Mains2023
An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at $x=+2~\mathrm{m}, its velocity is \mathrm{ - 4\widehat j} m/s. The object's velocity (v) and acceleration (a) at x=-2~\mathrm{m}$ will be
Options:
A) v=4\mathrm{\widehat i~m/s},a=8\mathrm{\widehat j~m/s^2}
B) v=4\mathrm{\widehat j~m/s},a=8\mathrm{\widehat i~m/s^2}
C) v=-4\mathrm{\widehat i~m/s},a=-8\mathrm{\widehat j~m/s^2}
D) v=-4\mathrm{\widehat j~m/s},a=8\mathrm{\widehat i~m/s^2}
87
MediumJEE Mains2023
A bullet of mass $0.1 \mathrm{~kg} moving horizontally with speed 400 \mathrm{~ms}^{-1} hits a wooden block of mass 3.9 \mathrm{~kg} kept on a horizontal rough surface. The bullet gets embedded into the block and moves 20 \mathrm{~m} before coming to rest. The coefficient of friction between the block and the surface is __________. (Given g=10 \mathrm{~m} / \mathrm{s}^{2}$ )
Options:
A) 0.65
B) 0.25
C) 0.50
D) 0.90
88
EasyJEE Mains2023
A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [take g = 10 ms$^{-2}$]
Options:
A) 3.4 ms$^{-1}
B) 13 ms$^{-1}
C) 22.4 ms$^{-1}
D) 17 ms$^{-1}
89
MediumJEE Mains2023
Identify the correct statements from the following : A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative. B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative. C. Work done by friction on a body sliding down an inclined plane is positive. D. Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero. E. Work done by the air resistance on an oscillating pendulum is negative. Choose the correct answer from the options given below :
Options:
A) A and C only
B) B and D only
C) B, D and E only
D) B and E only
90
EasyJEE Mains2023
A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m/s$^2$)
Options:
A) \frac{\pi}{2}
B) \frac{\pi}{6}
C) \frac{\pi}{4}
D) \frac{\pi}{3}
91
EasyJEE Mains2023
A stone is projected at angle $30^{\circ}$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be -
Options:
A) 1 : 4
B) 1 : 2
C) 4 : 3
D) 4 : 1
92
MediumJEE Mains2023
A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s. Then the ratio of extension in the spring to its natural length will be :
Options:
A) 1 : 2
B) 2 : 3
C) 2 : 5
D) 1 : 1
93
EasyJEE Mains2022
A ball is projected with kinetic energy E, at an angle of $60^{\circ}$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :
Options:
A) Zero
B) \frac{E}{2}
C) \frac{E}{4}
D) E
94
EasyJEE Mains2022
A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v) ?
Options:
A)
B)
C)
D)
95
MediumJEE Mains2022
A bullet of mass $200 \mathrm{~g} having initial kinetic energy 90 \mathrm{~J} is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to 40 \mathrm{~J} within 1 \mathrm{~s}$, the minimum length of the pool, the bullet has to travel so that it completely comes to rest is
Options:
A) 45 m
B) 90 m
C) 125 m
D) 25 m
96
MediumJEE Mains2022
A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is $60 \mathrm{~m}, then the magnitude of displacement would be : (Given \left.\cos 135^{\circ}=-0.7\right)
Options:
A) 42 m
B) 47 m
C) 19 m
D) 40 m
97
MediumJEE Mains2022
Sand is being dropped from a stationary dropper at a rate of $0.5 \,\mathrm{kgs}^{-1} on a conveyor belt moving with a velocity of 5 \mathrm{~ms}^{-1}$. The power needed to keep the belt moving with the same velocity will be :
Options:
A) 1.25 W
B) 2.5 W
C) 6.25 W
D) 12.5 W
98
MediumJEE Mains2022
A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k 2 rt 2 , where k is a constant. The power delivered to the particle by the force acting on it is given as
Options:
A) zero
B) mk
2
r
2
t
2
C) mk
2
r
2
t
D) mk
2
rt
99
EasyJEE Mains2022
As per the given figure, two blocks each of mass $250 \mathrm{~g} are connected to a spring of spring constant 2 \,\mathrm{Nm}^{-1}. If both are given velocity v$ in opposite directions, then maximum elongation of the spring is :
Options:
A) \frac{v}{2 \sqrt{2}}
B) \frac{v}{2}
C) \frac{v}{4}
D)
\frac{v}{\sqrt{2}}
100
MediumJEE Mains2022
A stone tide to a spring of length L is whirled in a vertical circle with the other end of the spring at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $\sqrt {x({u^2} - gL)} $. The value of x is -
Options:
A) 3
B) 2
C) 1
D) 5
101
EasyJEE Mains2022
A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms $-$1 gets embedded in it, then loss of kinetic energy will be :
Options:
A) 4.9 J
B) 9.8 J
C) 14.7 J
D) 19.6 J
102
MediumJEE Mains2022
A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is $\alpha with respect to point P. Which of the following graphs represent the correct relation between A and \alpha$ when ball goes from Q to R?
Options:
A)
B)
C)
D)
103
EasyJEE Mains2022
A body of mass $0.5 \mathrm{~kg} travels on straight line path with velocity v=\left(3 x^{2}+4\right) \mathrm{m} / \mathrm{s}. The net workdone by the force during its displacement from x=0 to x=2 \mathrm{~m}$ is :
Options:
A) 64 J
B) 60 J
C) 120 J
D) 128 J
104
MediumJEE Mains2022
A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega. The coefficient of static friction between the bottom of the beaker and the surface of the disc is \mu$. The beaker will revolve with the disc if :
Options:
A) R \le {{\mu g} \over {2{\omega ^2}}}
B) R \le {{\mu g} \over {{\omega ^2}}}
C) R \ge {{\mu g} \over {2{\omega ^2}}}
D) R \ge {{\mu g} \over {{\omega ^2}}}
105
EasyJEE Mains2022
In the given figure, the block of mass m is dropped from the point 'A'. The expression for kinetic energy of block when it reaches point 'B' is
Options:
A) {1 \over 2}mg\,{y_0}^2
B) {1 \over 2}mg\,{y^2}
C) mg(y - {y_0})
D) mg{y_0}
106
EasyJEE Mains2022
For a particle in uniform circular motion, the acceleration $\overrightarrow a at any point P(R, \theta) on the circular path of radius R is (when \theta$ is measured from the positive x-axis and v is uniform speed) :
Options:
A) - {{{v^2}} \over R}\sin \theta \widehat i + {{{v^2}} \over R}\cos \theta \widehat j
B) - {{{v^2}} \over R}\cos \theta \widehat i + {{{v^2}} \over R}\sin \theta \widehat j
C) - {{{v^2}} \over R}\cos \theta \widehat i - {{{v^2}} \over R}\sin \theta \widehat j
D) - {{{v^2}} \over R}\widehat i + {{{v^2}} \over R}\widehat j
107
MediumJEE Mains2022
A particle of mass 500 gm is moving in a straight line with velocity v = b x 5/2 . The work done by the net force during its displacement from x = 0 to x = 4 m is : (Take b = 0.25 m $-3/2 s -$1 ).
Options:
A) 2 J
B) 4 J
C) 8 J
D) 16 J
108
MediumJEE Mains2022
A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is
Options:
A) the same throughout the motion.
B) minimum at the highest position of the circular path.
C) minimum at the lowest position of the circular path.
D) minimum when the rope is in the horizontal position.
109
MediumJEE Mains2022
Arrange the four graphs in descending order of total work done; where W 1 , W 2 , W 3 and W 4 are the work done corresponding to figure a, b, c and d respectively.
Options:
A) W
3
> W
2
> W
1
> W
4
B) W
3
> W
2
> W
4
> W
1
C) W
2
> W
3
> W
4
> W
1
D) W
2
> W
3
> W
1
> W
4
110
EasyJEE Mains2022
A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :
Options:
A) 7.5 rad
B) 15 rad
C) 20 rad
D) 30 rad
111
MediumJEE Mains2022
A particle experiences a variable force $\overrightarrow F = \left( {4x\widehat i + 3{y^2}\widehat j} \right)$ in a horizontal x-y plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the x-y plane, then Kinetic Energy changes by :
Options:
A) 50.0 J
B) 12.5 J
C) 25.0 J
D) 0 J
112
EasyJEE Mains2022
A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is ${K \over \pi }$ rev./min. The value of K is : (Assume the string is massless and unstretchable)
Options:
A) 400
B) 300
C) 600
D) 800
113
EasyJEE Mains2021
A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of 0.8$\sqrt {gh} $. The value of workdone by the air-friction is :
Options:
A) -$0.68 mgh
B) mgh
C) 1.64 mgh
D) 0.64 mgh
114
MediumJEE Mains2021
A huge circular arc of length 4.4 ly subtends an angle '4s' at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second? Given : 1 ly = 9.46 $\times 10 15 m 1 AU = 1.5 \times$ 10 11 m
Options:
A) 4.1 $\times$ 10
8
s
B) 4.5 $\times$ 10
10
s
C) 3.5 $\times$ 10
6
s
D) 7.2 $\times$ 10
8
s
115
MediumJEE Mains2021
A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1 : 2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is :-
Options:
A) {{1 \over 3}}
B) {{2 \over 3}}
C) {{1 \over 8}}
D) {{1 \over 4}}
116
MediumJEE Mains2021
A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that $r = {L \over {\sqrt 2 }}$. The speed of particle will be :
Options:
A) {\sqrt {rg} }
B) {\sqrt {2rg} }
C) {2\sqrt {rg} }
D) {\sqrt {{{rg} \over 2}} }
117
MediumJEE Mains2021
Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that E mech = 8 J, the incorrect statement for this system is : [ where K.E. = kinetic energy ]
Options:
A) at x > x
4
K.E. is constant throughout the region.
B) at x < x
1
, K.E. is smallest and the particle is moving at the slowest speed.
C) at x = x
2
, K.E. is greatest and the particle is moving at the fastest speed.
D) at x = x
3
, K.E. = 4 J.
118
MediumJEE Mains2021
The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30$^\circ banked road at maximum possible speed without skidding is ____________ \times 10 3 kg m/s 2 . [Given cos30^\circ = 0.87, \mu$ s = 0.2]
Options:
A) 12.4
B) 7.2
C) 6.96
D) 10.2
119
MediumJEE Mains2021
An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :
Options:
A) {\left( {{{9P} \over {8m}}} \right)^{{1 \over 2}}}{t^{{3 \over 2}}}
B) {\left( {{{8P} \over {9m}}} \right)^{{1 \over 2}}}{t^{{2 \over 3}}}
C) {\left( {{{9m} \over {8P}}} \right)^{{1 \over 2}}}{t^{{3 \over 2}}}
D) {\left( {{{8P} \over {9m}}} \right)^{{1 \over 2}}}{t^{{3 \over 2}}}
120
MediumJEE Mains2021
A particle of mass m moves in a circular orbit under the central potential field, $U(r) = - {C \over r}, where C is a positive constant. The correct radius -$ velocity graph of the particle's motion is :
Options:
A)
B)
C)
D)
121
EasyJEE Mains2021
A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take g = 9.8 ms $-$2 )
Options:
A) +627.2 J
B) -$62720.0 J
C) -$627.2 J
D) 784.0 J
122
MediumJEE Mains2021
A modern grand - prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is $\mu$ s , then the magnitude of negative lift F L acting downwards on the car is : (Assume forces on the four tyres are identical and g = acceleration due to gravity)
Options:
A) m\left( {g - {{{v^2}} \over {{\mu _s}R}}} \right)
B) - m\left( {g + {{{v^2}} \over {{\mu _s}R}}} \right)
C) m\left( {{{{v^2}} \over {{\mu _s}R}} - g} \right)
D) m\left( {{{{v^2}} \over {{\mu _s}R}} + g} \right)
123
MediumJEE Mains2021
A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to :
Options:
A) {t^{{3 \over 2}}}
B) {t^{{1 \over 2}}}
C) {t^{{1 \over 4}}}
D) {t^{{3 \over 4}}}
124
MediumJEE Mains2021
Statement I : A cyclist is moving on an unbanked road with a speed of 7 kmh $-1 and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s 2 ) Statement II : If the road is banked at an angle of 45^\circ, cyclist can cross the curve of 2m radius with the speed of 18.5 kmh -$1 without slipping. In the light of the above statements, choose the correct answer from the options given below.
Options:
A) Statement I is incorrect and statement II is correct
B) Both statement I and statement II are true
C) Statement I is correct and statement II is incorrect
D) Both statement I and statement II are false
125
MediumJEE Mains2021
A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :-
Options:
A) t
2/3
B) t
3/2
C) t
D) t
1/2
126
EasyJEE Mains2021
A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is :
Options:
A) 9.859 $\times 10
-$2
N
B) 0.0314 N
C) 9.859 $\times 10
-$4
N
D) 6.28 $\times 10
-$3
N
127
EasyJEE Mains2021
A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of 20 ms -1 . The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now?
Options:
A) 14.41 ms
$-$1
B) 19.0 ms
$-$1
C) 4.47 ms
$-$1
D) 1.00 ms
$-$1
128
MediumJEE Mains2021
A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R 3 . Its time period of revolution will be given by :
Options:
A) T \propto {R^{{4 \over 3}}}
B) T \propto {R^{{5 \over 2}}}
C) T \propto {R^{{3 \over 2}}}
D) T \propto {R^2}
129
MediumJEE Mains2020
If the potential energy between two molecules is given by U = $ - {A \over {{r^6}}} + {B \over {{r^{12}}}}$, then at equilibrium, separation between molecules, and the potential energy are :
Options:
A) {\left( {{{2B} \over A}} \right)^{1/6}}, - {{{A^2}} \over {4B}}
B) {\left( {{{2B} \over A}} \right)^{1/6}}, - {{{A^2}} \over {2B}}
C) {\left( {{B \over A}} \right)^{1/6}},0
D) {\left( {{B \over {2A}}} \right)^{1/6}}, - {{{A^2}} \over {2B}}
130
MediumJEE Mains2020
A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms –2 ) is of the order of :
Options:
A) 10
-3
B) 10
-1
C) 10
-2
D) 10
-4
131
MediumJEE Mains2020
A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?
Options:
A) 5690 J
B) 5250 J
C) 2780 J
D) 3280 J
132
MediumJEE Mains2020
A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = 4Cx 2 and rotating with angular speed $\omega (see figure). The value of \omega $ is (neglect friction) :
Options:
A) 2\sqrt {2gC}
B) 2\sqrt {gC}
C) \sqrt {{{2gC} \over {ab}}}
D) \sqrt {{{2g} \over C}}
133
MediumJEE Mains2020
A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) :
Options:
A)
B)
C)
D)
134
MediumJEE Mains2020
A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length $\ell . The other end is fixed. The system is given an angular speed \omega $ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is :
Options:
A) {{m\ell {\omega ^2}} \over {k - m{\omega ^2}}}
B) {{m\ell {\omega ^2}} \over {k - m{\omega}}}
C) {{m\ell {\omega ^2}} \over {k + m{\omega ^2}}}
D) {{m\ell {\omega ^2}} \over {k + m{\omega}}}
135
MediumJEE Mains2020
Consider a force $\overrightarrow F = - x\widehat i + y\widehat j$ . The work done by this force in moving a particle from point A(1, 0) to B(0, 1) along the line segment is : (all quantities are in SI units)
Options:
A) 2
B) {1 \over 2}
C) 1
D) {3 \over 2}
136
MediumJEE Mains2019
A smooth wire of length 2$\pi r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed \omega about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of \omega $ 2 is equal to -
Options:
A) {{\sqrt 3 g} \over {2r}}
B) {{2g} \over {\left( {r\sqrt 3 } \right)}}
C) {{\left( {g\sqrt 3 } \right)} \over r}
D) {{2g} \over r}
137
MediumJEE Mains2020
An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg, The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s. The frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10 m/s 2 ) must be at least :
Options:
A) 48000 W
B) 62360 W
C) 56300 W
D) 66000 W
138
MediumJEE Mains2019
A body is projected at t = 0 with a velocity 10 ms –1 at an angle of 60 o with the horizontal. The radius of curvature of its trajectory at t = 1s is R. neglecting air resistance and taking acceleration due to gravity g = 10 ms –2 , the value of R is :
Options:
A) 2.8 m
B) 5.1 m
C) 2.5 m
D) 10.3 m
139
MediumJEE Mains2020
A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : (1 HP = 746 W, g = 10 ms -2 )
Options:
A) 1.5 ms
-1
B) 1.7 ms
-1
C) 2.0 ms
-1
D) 1.9 ms
-1
140
MediumJEE Mains2019
A particle is moving along a circular path with a constant speed of 10 ms –1 . What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60 o around the centre of the circle?
Options:
A) zero
B) 10 m/s
C) 10\sqrt 2 m/s
D) 10\sqrt 3 m/s
141
MediumJEE Mains2019
A uniform cable of mass 'M' and length 'L' is placed on a horizontal surface such that its (1/n) th part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be :
Options:
A) {{2MgL} \over {{n^2}}}
B) nMgL
C) {{MgL} \over {2{n^2}}}
D) {{MgL} \over {{n^2}}}
142
MediumJEE Mains2018
A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of $3.5$ revolutions per second. A coin placed at a distnce of 1.25 cm from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is : (g = 10 m/s 2 )
Options:
A) 0.5
B) 0.3
C) 0.7
D) 0.6
143
MediumJEE Mains2019
A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3m is :
Options:
A) 6.5 J
B) 2.5 J
C) 5 J
D) 4 J
144
MediumJEE Mains2017
A conical pendulum of length 1 m makes an angle $\theta $ = 45 o w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be: (Take g = 10 ms −2 )
Options:
A) 0.4 m/s
B) 4 m/s
C) 0.2 m/s
D) 2 m/s
145
MediumJEE Mains2019
A particle which is experiencing a force, given by $\overrightarrow F = 3\widehat i - 12\widehat j, undergoes a displacement of \overrightarrow d = 4\overrightarrow i $ particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement ?
Options:
A) 9 J
B) 10 J
C) 12 J
D) 15 J
146
MediumJEE Mains2012
Two cars of masses m 1 and m 2 are moving in circles of radii r 1 and r 2 , respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is
Options:
A) m
1
r
1
: m
2
r
2
B) m
1
: m
2
C) r
1
: r
2
D) 1 : 1
147
MediumJEE Mains2019
A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in figure. Work done by normal reaction on block in time is -
Options:
A) {{m{g^2}{t^2}} \over 8}
B) {{3m{g^2}{t^2}} \over 8}
C) - {{m{g^2}{t^2}} \over 8}
D) 0
148
MediumJEE Mains2010
For a particle in uniform circular motion the acceleration $\overrightarrow a $ at a point P(R, θ) on the circle of radius R is (here θ is measured from the x–axis)
Options:
A) - {{{v^2}} \over R}\cos \theta \widehat i + {{{v^2}} \over R}\sin \theta \widehat j
B) - {{{v^2}} \over R}\sin \theta \widehat i + {{{v^2}} \over R}\cos \theta \widehat j
C) - {{{v^2}} \over R}\cos \theta \widehat i - {{{v^2}} \over R}\sin \theta \widehat j
D) {{{v^2}} \over R}\widehat i + {{{v^2}} \over R}\widehat j
149
MediumJEE Mains2019
A force acts on a 2 kg object so that its position is given as a function of time as x = 3t 2 + 5. What is the work done by this force in first 5 seconds ?
Options:
A) 850 J
B) 950 J
C) 875 J
D) 900 J
150
MediumJEE Mains2010
A point $P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out a length s = {t^3} + 5, where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of 'P' when t=2 s$ is nearly.
Options:
A) 13m/{s_2}
B) 12m/{s^2}
C) 7.2m{s^2}
D) 14m/{s^2}
151
MediumJEE Mains2019
A block of mass m, lying on a smooth horizontal surface, is attached to a sring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is :
Options:
A) {{2F} \over {\sqrt {mk} }}
B) {F \over {\pi \sqrt {mk} }}
C) {{\pi F} \over {\sqrt {mk} }}
D) {F \over {\sqrt {mk} }}
152
MediumJEE Mains2004
Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?
Options:
A) The velocity vector is tangent to the circle.
B) The acceleration vector is tangent to the circle.
C) The acceleration vector points to the centre of the circle.
D) The velocity and acceleration vectors are perpendicular to each other.
153
MediumJEE Mains2018
Two particles of the same mass m are moving in circular orbits because of force, given by $F\left( r \right) = {{ - 16} \over r} - {r^3}$ The first particle is at a distance r = 1, and the second, at r = 4. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to :
Options:
A) 6 \times {10^{ - 2}}
B) 3 \times {10^{ - 3}}
C) {10^{ - 1}}
D) 6 \times {10^{ 2}}
154
MediumJEE Mains2002
The minimum velocity (in $m{s^{ - 1}}) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6$ to avoid skidding is
Options:
A) 60
B) 30
C) 15
D) 25
155
MediumJEE Mains2018
A body of mass m starts moving from rest along x-axis so that its velocity varies as $\upsilon = a\sqrt s $ where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is :
Options:
A) {1 \over 8}\,$ m a
4
t
2
B) 8 m a
4
t
2
C) 4 m a
4
t
2
D) {1 \over 4}\,$ m a
4
t
2
156
EasyInteger TypeJEE Mains2025
A particle of charge 1.6 \mu \mathrm{C} and mass 16 \mu \mathrm{~g} is present in a strong magnetic field of 6.28 T . The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is _________ s. (\pi=3.14)
Answer: Enter a numeric value
157
MediumJEE Mains2018
A particle is moving in a circular path of radius $a under the action of an attractive potential U = - {k \over {2{r^2}}}$ Its total energy is:
Options:
A) - {3 \over 2}{k \over {{a^2}}}
B) Zero
C) - {k \over {4{a^2}}}
D) {k \over {2{a^2}}}
158
MediumInteger TypeJEE Mains2025
A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes \left(\frac{3}{\pi}\right) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is __________ ML.
Answer: Enter a numeric value
159
MediumJEE Mains2017
An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t $ \to \infty $ is :
Options:
A) 3h
B) \infty
C) {5 \over 3}$h
D) {8 \over 3}$h
160
MediumInteger TypeJEE Mains2025
A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is \sqrt{\frac{\mathrm{F}}{\alpha \mathrm{M}}} in SI unit. The value of \alpha is _________.
Answer: Enter a numeric value
161
MediumJEE Mains2017
A body of mass m = 10 –2 kg is moving in a medium and experiences a frictional force F = –kv 2 . Its initial speed is v 0 = 10 ms –1 . If, after 10 s, its energy is ${1 \over 8}mv_0^2$, the value of k will be:
Options:
A) 10
-1
kg m
-1
s
-1
B) 10
-3
kg m
-1
C) 10
-3
kg s
-1
D) 10
-4
kg m
-1
162
HardInteger TypeJEE Mains2024
A particle is moving in a circle of radius $50 \mathrm{~cm} in such a way that at any instant the normal and tangential components of it's acceleration are equal. If its speed at \mathrm{t}=0 is 4 \mathrm{~m} / \mathrm{s}, the time taken to complete the first revolution will be \frac{1}{\alpha}\left[1-e^{-2 \pi}\right] \mathrm{s}, where \alpha=$ _________.
Answer: Enter a numeric value
163
MediumJEE Mains2017
A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be:
Options:
A) 18 J
B) 4.5 J
C) 22 J
D) 9 J
164
EasyInteger TypeJEE Mains2023
A stone tied to 180 \mathrm{~cm} long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is \frac{1936}{x} ms^{-2}. The value of x ________. (Take \pi=\frac{22}{7} )
Answer: Enter a numeric value
165
MediumJEE Mains2016
Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on the body in first two seconds of the motion is :
Options:
A) 12000 J
B) -$ 12000 J
C) -$ 4500 J
D) -$ 9300 J
166
HardInteger TypeJEE Mains2023
A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54 km/hr is $t(1-e^{-\pi/2})s$. The value of t is ____________.
Answer: Enter a numeric value
167
MediumJEE Mains2016
A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n 2 R t 2 where n is a constant. The power delivered to the particle by the force acting on it, is :
Options:
A) M n
2
R
2
t
B) M n R
2
t
C) M n R
2
t
2
D) {1 \over 2}$ M n
2
R
2
t
2
168
EasyInteger TypeJEE Mains2022
A person starts his journey from centre 'O' of the park and comes back to the same position following path OPQO as shown in the figure. The radius of path taken by the person is 200 m and he takes 3 min 58 sec to complete his journey. The average speed of the person is _____________ ms $-1 . (take \pi$ = 3.14)
Answer: Enter a numeric value
169
MediumJEE Mains2016
A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force ${W \over 20} on the car. While moving uphill on the road at a speed of 10 ms −1 , the car needs power P. If it needs power {p \over 2} while moving downhill at speed v then value of \upsilon $ is :
Options:
A) 20 ms
$-$1
B) 15 ms
$-$1
C) 10 ms
$-$1
D) 5 ms
$-$1
170
HardInteger TypeJEE Mains2022
A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed ${v \over 3} and the bob just completes the vertical circle. The value of v is ___________ ms -$1 . (if g = 10 m/s 2 ).
Answer: Enter a numeric value
171
MediumJEE Mains2016
A point particle of mass $m, moves long the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals \mu . The particle is released, from rest from the point P and it comes to rest at point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other , and no energy is lost when particle changes direction from PQ to QR. The value of the coefficient of friction \mu and the distance x (=QR),$ are, respectively close to:
Options:
A) 0.29 and 3.5 m
B) 0.29 and 6.5 m
C) 0.2 and 6.5 m
D) 0.2 and 3.5 m
172
MediumInteger TypeJEE Mains2022
A curved in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ___________ m/s.
Answer: Enter a numeric value
173
MediumJEE Mains2016
A person trying to lose weight by burning fat lifts a mass of $10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies 3.8 \times {10^7}J of energy per kg which is converted to mechanical energy with a 20\% efficiency rate. Take g = 9.8\,m{s^{ - 2}}$ :
Options:
A) 9.89 \times {10^{ - 3}}\,\,kg
B) 12.89 \times {10^{ - 3}}\,kg
C) 2.45 \times {10^{ - 3}}\,\,kg
D) 6.45 \times {10^{ - 3}}\,\,kg
174
MediumInteger TypeJEE Mains2021
A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ________ m/s. (Take g = 10 m/s 2 )
Answer: Enter a numeric value
175
MediumJEE Mains2014
When a rubber-band is stretched by a distance $x, it exerts restoring force of magnitude F = ax + b{x^2} where a and b are constants. The work done in stretching the unstretched rubber-band by L$ is :
Options:
A) a{L^2} + b{L^3}
B) {1 \over 2}\left( {a{L^2} + b{L^3}} \right)
C) {{a{L^2}} \over 2} + {{b{L^3}} \over 3}
D) {1 \over 2}\left( {{{a{L^2}} \over 2} + {{b{L^3}} \over 3}} \right)
176
MediumMHT CET2025
A stone of mass ' m ' kg is tied to a string of length ' L ' m and moved in a vertical circle of radius 49 cm in a vertical plane. If it completes 30 revolutions per minute, the tension in the string when it is at the lowermost point is nearly [Take \pi^2=10 and acceleration due to gravity, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 ]
Options:
A) (90 \mathrm{~m}) \mathrm{N}
B) \quad(60 \mathrm{~m}) \mathrm{N}
C) (45 m) \mathrm{N}
D) (15 m) \mathrm{N}
177
MediumJEE Mains2012
This question has Statement $1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. If two springs {S_1} and {S_2} of force constants {k_1} and {k_2}, respectively, are stretched by the same force, it is found that more work is done on spring {S_1} than on spring {S_2}. STATEMENT 1: If stretched by the same amount work done on {S_1}, Work done on {S_1} is more than {S_2} STATEMENT 2: {k_1} < {k_2}
Options:
A) Statement 1 is false, Statement 2 is true
B) Statement 1 is true, Statement 2 is false
C) Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1
D) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1
178
MediumMHT CET2025
A point mass ' m ' attached at one end of a massless, inextensible string of length ' l ' performs a vertical circular motion and the string rotates in vertical plane, as shown in the diagram. The increase in the centripetal acceleration of the point mass when it moves from point A to point C is [ \mathrm{g}= acceleration due to gravity.]
Options:
A) 3 g
B) 2 g
C) g
D) \frac{\mathrm{g}}{2}
179
MediumJEE Mains2010
The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U\left( x \right) = {a \over {{x^{12}}}} - {b \over {{x^6}}}, where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is D = \left[ {U\left( {x = \infty } \right) - {U_{at\,\,equilibrium}}} \right],\,\,D$ is
Options:
A) {{{b^2}} \over {2a}}
B) {{{b^2}} \over {12a}}
C) {{{b^2}} \over {4a}}
D) {{{b^2}} \over {6a}}
180
MediumMHT CET2025
An inextensible string of length ' l ' fixed at one end, carries a mass ' m ' at the other end. If the string makes \frac{1}{\pi} revolutions per second around the vertical axis through the fixed end, the tension in the string is [The string makes an angle \theta with the vertical]
Options:
A) 16 ml
B) 8 ml
C) 4 ml
D) 2 ml
181
MediumJEE Mains2008
An athlete in the olympic games covers a distance of $100 m in 10 s.$ His kinetic energy can be estimated to be in the range
Options:
A) 200J-500J
B) 2 \times {10^5}J - 3 \times {10^5}J
C) 20,000J - 50,000J
D) 2,000J - 5,000J
182
MediumMHT CET2025
A particle describes a horizontal circle on smooth inner surface of a cone as shown in figure. If the height of the circle above the vertex is 10 cm . The speed of the particle is \left(\mathrm{g}\right., acceleration due to gravity \left.=10 \mathrm{~m} / \mathrm{s}^2\right)
Options:
A) 2 \mathrm{~m} / \mathrm{s}
B) 1.5 \mathrm{~m} / \mathrm{s}
C) 1 \mathrm{~m} / \mathrm{s}
D) 0.5 \mathrm{~m} / \mathrm{s}
183
MediumJEE Mains2007
A $2 kg block slides on a horizontal floor with a speed of 4m/s. It strikes a uncompressed spring, and compress it till the block is motionless. The kinetic friction force is 15N and spring constant is 10, 000 N/m.$ The spring compresses by
Options:
A) 8.5cm
B) 5.5cm
C) 2.5cm
D) 11.0cm
184
MediumMHT CET2025
Two stones of masses m and 3 m are whirled in horizontal circles, the heavier one in a radius \left(\frac{\mathrm{r}}{3}\right) and lighter one in a radius r . The tangential speed of lighter stone is ' n ' times the value of heavier stone. When the magnitude of centripetal force becomes equal the value of n is
Options:
A) 4
B) 3
C) 2
D) 1
185
MediumJEE Mains2007
A particle is projected at $60^\circ $ to the horizontal with a kinetic energy K. The kinetic energy at the highest point is
Options:
A) K/2
B) K
C) Zero
D) K/4
186
MediumMHT CET2025
A motor cyclist has to rotate in horizontal circles inside the cylindrical wall of inner radius ' R ' metre. If the coefficient of friction between the wall and the tyres is ' \mu_{\mathrm{s}} ', then the minimum speed required is ( \mathrm{g}= acceleration due to gravity)
Options:
A) \sqrt{\mu_{\mathrm{r}} \mathrm{Rg}}
B) \sqrt{\frac{\mathrm{Rg}}{\mu_{\mathrm{s}}}}
C) \sqrt{\frac{\mu_{\mathrm{s}}}{\mathrm{Rg}}}
D) \sqrt{\frac{R^2 g}{\mu_s}}
187
MediumJEE Mains2006
A ball of mass $0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes upto 2 m height further, find the magnitude of the force. (consider g = 10\,m/{s^2}$).
Options:
A) 4N
B) 16 N
C) 20 N
D) 22 N
188
MediumMHT CET2025
The figure shows two masses ' m ' and ' M ' connected by a light string that passes through { }_a small hole ' O ' at the centre of the table. Mass ' m ' is moved round in a horizontal circle with ' O ' as the centre. The frequency with which ' m ' should be revolved so that ' M ' remains stationary is ( \mathrm{g}= gravitational acceleration)
Options:
A) \frac{1}{\pi} \sqrt{\frac{\mathrm{ML}}{\mathrm{mg}}}
B) \frac{1}{2 \pi} \sqrt{\frac{\mathrm{Mg}}{\mathrm{mL}}}
C) \frac{1}{\pi} \sqrt{\frac{\mathrm{Mg}}{\mathrm{mL}}}
D) \frac{1}{2 \pi} \sqrt{\frac{\mathrm{ML}}{\mathrm{mg}}}
189
MediumJEE Mains2006
A mass of $M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of {45^ \circ }$ with the initial vertical direction is
Options:
A) Mg\left( {\sqrt 2 + 1} \right)
B) Mg\sqrt 2
C) {{Mg} \over {\sqrt 2 }}
D) Mg\left( {\sqrt 2 - 1} \right)
190
MediumMHT CET2025
Radius of curved road is ' R ', width of road is ' b '. The outer edge of road is raised by ' h ' with respect to inner edge so that a car with velocity ' V ' can pass safe over it, then value of ' h ' is ( \mathrm{g}= acceleration due to gravity)
Options:
A) \frac{\mathrm{V}^2 \mathrm{~b}}{\mathrm{Rg}}
B) \frac{\mathrm{V}}{\mathrm{Rgb}}
C) \frac{V^2 R}{g}
D) \frac{V^2 b}{g}
191
MediumJEE Mains2006
A particle of mass $100g is thrown vertically upwards with a speed of 5 m/s$. The work done by the force of gravity during the time the particle goes up is
Options:
A) -0.5J
B) -1.25J
C) 1.25J
D) 0.5J
192
MediumMHT CET2025
Two bodies of mass 10 kg and 5 kg are moving in concentric circular orbits of radii ' R ' and ' r ' respectively such that their periods are same. The ratio between their centripetal acceleration is
Options:
A) \mathrm{R} / \mathrm{r}
B) \quad \mathrm{r} / \mathrm{R}
C) \mathrm{R}^2 / \mathrm{r}^2
D) r^2 / R^2
193
MediumJEE Mains2006
The potential energy of a $1 kg particle free to move along the x-axis is given by V\left( x \right) = \left( {{{{x^4}} \over 4} - {{{x^2}} \over 2}} \right)J. The total mechanical energy of the particle is 2J. Then, the maximum speed (in m/s$) is
Options:
A) {3 \over {\sqrt 2 }}
B) {\sqrt 2 }
C) {1 \over {\sqrt 2 }}
D) 2
194
MediumMHT CET2025
A car is driven on the banked road of radius of curvature 20 m with maximum safe speed. In order to increase its safety speed by 20 \%, without changing the angle of banking, the increase in the radius of curvature will be [Assume friction is same on the road]
Options:
A) 28.8 m
B) 14.4 m
C) 8.8 m
D) 4.8 m
195
MediumJEE Mains2005
A body of mass $m is accelerated uniformly from rest to a speed v in a time T.$ The instantaneous power delivered to the body as a function of time is given by
Options:
A) {{m{v^2}} \over {{T^2}}}.{t^2}
B) {{m{v^2}} \over {{T^2}}}.t
C) {1 \over 2}{{m{v^2}} \over {{T^2}}}.{t^2}
D) {1 \over 2}{{m{v^2}} \over {{T^2}}}.t
196
MediumMHT CET2025
A vehicle is moving with uniform speed along 3 different shaped roads as horizontal, concave and convex. The surface of road on which, the normal reaction on vehicle is maximum is
Options:
A) convex
B) concave
C) horizontal
D) same on all the 3 surface
197
MediumJEE Mains2005
A bullet fired into a fixed target loses half of its velocity after penetrating $3 cm.$ How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?
Options:
A) 2.0 cm
B) 3.0 cm
C) 1.0 cm
D) 1.5 cm
198
MediumMHT CET2025
A vehicle is moving with a constant speed of 10 \mathrm{~m} / \mathrm{s} in a circular horizontal track of radius 20 m . A bob is suspended from the roof of a vehicle by a massless string. The angle made by the string with the vertical will be (acceleration due to gravity, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )
Options:
A) \tan ^{-1}(0.5)
B) \tan ^{-1}(0.6)
C) \tan ^{-1}(0.7)
D) \tan ^{-1}(0.8)
199
MediumJEE Mains2005
A spherical ball of mass $20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m$ above the ground. The velocity attained by the ball is
Options:
A) 20 m/s
B) 40 m/s
C) 10\sqrt {30} \,\,\,m/s
D) 10\,\,m/s
200
MediumMHT CET2025
A body of mass 100 gram is tied to a spring of spring constant 8 \mathrm{~N} / \mathrm{m}, while the other end of a spring is fixed. If the body moves in a circular path on smooth horizontal surface with constant angular speed 8 \mathrm{rad} / \mathrm{s} then the ratio of extension in the spring to its natured length will be
Options:
A) 1: 1
B) 8: 1
C) 2: 1
D) 4: 1
201
MediumJEE Mains2005
The upper half of an inclined plane with inclination $\phi $ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
Options:
A) 2\,\cos \,\,\phi
B) 2\,sin\,\,\phi
C) \,\tan \,\,\phi
D) 2\,\tan \,\,\phi
202
MediumMHT CET2025
A simple pendulum oscillates with an angular amplitude \theta. If the maximum tension in the string is 4 times the minimum tension then the value of \theta is
Options:
A) \cos ^{-1}(0.75)
B) \cos ^{-1}(0.5)
C) \sin ^{-1}(0.5)
D) \sin ^{-1}(0.75)
203
MediumJEE Mains2004
A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to
Options:
A) x
B) {e^x}
C) {x^2}
D) {\log _e}x
204
MediumMHT CET2025
A pendulum bob has a speed 4 \mathrm{~m} / \mathrm{s} at its lowest position. The pendulum is 1 m long. When the length of the string makes an angle of 60^{\circ} with the vertical, the speed of the bob at that position is (acceleration due to gravity, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \cos 60^{\circ}=0.5 )
Options:
A) 6 \mathrm{~m} / \mathrm{s}
B) \sqrt{3} \mathrm{~m} / \mathrm{s}
C) \sqrt{6} \mathrm{~m} / \mathrm{s}
D) 3 \mathrm{~m} / \mathrm{s}
205
MediumJEE Mains2004
A uniform chain of length $2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg.$ What is the work done in pulling the entire chain on the table?
Options:
A) 12 J
B) 3.6 J
C) 7.2 J
D) 1200 J
206
MediumMHT CET2025
A wheel initially at rest, begins to rotate about its axis with constant angular acceleration. If it rotates through an angle \theta_1 in first 2 s and a further angle \theta_2 in the next 2 s , the ratio \theta_1: \theta_2 is
Options:
A) 1: 6
B) 6: 1
C) 3: 1
D) 1: 3
207
MediumJEE Mains2004
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particles takes place in a plane. It follows that
Options:
A) its kinetic energy is constant
B) is acceleration is constant
C) its velocity is constant
D) it moves in a straight line
208
MediumMHT CET2025
For a particle moving in a circle with constant angular speed, which of the following statements is 'false'?
Options:
A) The velocity vector is tangent to the circle.
B) The acceleration vector is tangent to the circle.
C) The velocity and acceleration vectors are perpendicular to each other.
D) The acceleration vector points to the centre of the circle.
209
MediumJEE Mains2004
A body of mass $' m ', acceleration uniformly from rest to '{v_1}' in time {T}$. The instantaneous power delivered to the body as a function of time is given by
Options:
A) {{m{v_1}{t^2}} \over {{T}}}
B) {{mv_1^2t} \over {T^2}}
C) {{m{v_1}t} \over {{T}}}
D) {{mv_1^2t} \over {{T}}}
210
MediumMHT CET2025
A particle performing uniform circular motion of radius \frac{\pi}{2} \mathrm{~m} makes x revolutions in time t. Its tangential velocity is
Options:
A) \frac{x}{\pi t}
B) \frac{\pi^2}{x t}
C) \frac{\pi^2 x}{t}
D) \frac{\pi x}{t}
211
MediumJEE Mains2004
A force $\overrightarrow F = \left( {5\overrightarrow i + 3\overrightarrow j + 2\overrightarrow k } \right)N is applied over a particle which displaces it from its origin to the point \overrightarrow r = \left( {2\overrightarrow i - \overrightarrow j } \right)m.$ The work done on the particle in joules is
Options:
A) +10
B) +7
C) -7
D) +13
212
MediumMHT CET2025
A weightless thread can bear tension up to 3.7 kg wt. A stone of mass 500 gram is tied to it and revolved in circular path of radius 4 m in vertical plane. Maximum angular velocity of the stone will be (acceleration due to gravity, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )
Options:
A) 16 \mathrm{rad} / \mathrm{s}
B) 4 \mathrm{rad} / \mathrm{s}
C) 2 \mathrm{rad} / \mathrm{s}
D) 8 \mathrm{rad} / \mathrm{s}
213
MediumJEE Mains2003
A wire suspended vertically from one of its ends is stretched by attaching a weight of $200N to the lower end. The weight stretches the wire by 1 mm.$ Then the elastic energy stored in the wire is
Options:
A) 0.2 J
B) 10 J
C) 20 J
D) 0.1 J
214
MediumMHT CET2025
When a ceiling fan is switched off, its angular velocity falls to \left(\frac{1}{3}\right)^{\text {rd }} while it makes 24 rotations. How many more rotations will it make before coming to rest?
Options:
A) 3
B) 6
C) 9
D) 12
215
MediumJEE Mains2003
A spring of spring constant $5 \times {10^3}\,N/m is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm$ is
Options:
A) 12.50 N-m
B) 18.75 N-m
C) 25.00 N-m
D) 625 N-m
216
MediumMHT CET2024
The linear speed of a particle at the equator of the earth due to its spin motion is ' V '. The linear speed of the particle at latitude 30^{\circ} is $\left[\begin{array}{l} \sin 30^{\circ}=\cos 60^{\circ}=1 / 2 \\ \cos 30^{\circ}=\sin 60^{\circ}=\sqrt{3} / 2 \end{array}\right]
Options:
A) \frac{\mathrm{V}}{\sqrt{2}}
B) \frac{\mathrm{V}}{2}
C) \frac{\sqrt{3}}{2} \mathrm{v}
D) \mathrm{V}
217
MediumJEE Mains2003
A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $'t'$ is proportional to
Options:
A) {t^{3/4}}
B) {t^{3/2}}
C) {t^{1/4}}
D) {t^{1/2}}
218
MediumMHT CET2024
Two objects of masses ' m_1 ' and ' m_2 ' are moving in the circles of radii ' r_1 ' and ' r_2 ' respectively. Their respective angular speeds ' \omega_1 ' and ' \omega_2 ' are such that they both complete one revolution in the same time ' t '. The ratio of linear speed of ' m_2 ' to that of ' m_1 ' is
Options:
A) \omega_1: \omega_2
B) \mathrm{T}_2: \mathrm{T}_1
C) \mathrm{m}_1: \mathrm{m}_2
D) \mathrm{r_2: r_1}
219
MediumJEE Mains2002
A spring of force constant $800 N/m has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm$ is
Options:
A) 16J
B) 8J
C) 32J
D) 24J
220
MediumMHT CET2024
A body performing uniform circular motion of radius ' R ' has frequency ' n '. Its centripetal acceleration per unit radius is proportional to (n)^x. The value of x is
Options:
A) 1
B) 2
C) -1
D) -2
221
MediumJEE Mains2002
A ball whose kinetic energy E, is projected at an angle of $45^\circ $ to the horizontal. The kinetic energy of the ball at the highest point of its height will be
Options:
A) E
B) {E \over {\sqrt 2 }}
C) {E \over 2}
D) zero
222
MediumMHT CET2024
A particle starting from rest moves along the circumference of a circle of radius ' r ' with angular acceleration ' \alpha '. The magnitude of the average velocity in time it completes the small angular displacement ' \theta ' is
Options:
A) \frac{r^2}{2 \alpha \theta}
B) \frac{\mathrm{r}}{2 \alpha \theta}
C) \frac{\mathrm{r} \alpha \theta}{2}
D) \frac{\mathrm{r}}{\sqrt{2}} \sqrt{\alpha \theta}
223
MediumJEE Mains2002
If a body looses half of its velocity on penetrating $3 cm$ in a wooden block, then how much will it penetrate more before coming to rest?
Options:
A) 1 cm
B) 2 cm
C) 3 cm
D) 4 cm
224
MediumMHT CET2024
A particle is moving in a circle with uniform speed. It has constant
Options:
A) velocity.
B) acceleration.
C) kinetic energy.
D) displacement.
225
EasyInteger TypeJEE Mains2026
A 1 kg block subjected to two simultaneous forces (2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}) \mathrm{N} and (3 \hat{\mathrm{i}}-\hat{\mathrm{j}}-2 \hat{\mathrm{k}}) \mathrm{N} is moved a distance of 25 m along (3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}) direction. The work done in this process is \_\_\_\_ J.
Answer: Enter a numeric value
226
MediumMHT CET2024
A particle of mass ' m ' is performing uniform circular motion along a circular path of radius ' r '. Its angular momentum about the axis passing through the centre and perpendicular to the plane is ' L '. The kinetic energy of the particle is
Options:
A) \frac{L^2}{2 Mr^2}
B) \frac{2 \mathrm{~L}^2}{\mathrm{mr}^2}
C) \frac{\mathrm{L}^2}{\mathrm{mr}^2}
D) \frac{2 \mathrm{~L}^2}{3 \mathrm{mr}^2}
227
EasyInteger TypeJEE Mains2026
A body of mass 2 kg begins to move under the influence of time dependent force \overrightarrow{\mathrm{F}}=\left(2 \mathrm{t} \hat{\mathrm{i}}+6 \mathrm{t}^2 \hat{\mathrm{j}}\right) \mathrm{N}, where \hat{\mathrm{i}} and \hat{\mathrm{j}} are unit vectors along x and y -axis respectively. The power produced by the force at t=2 \mathrm{~s} is \_\_\_\_ W.
Answer: Enter a numeric value
228
MediumMHT CET2024
A particle of mass ' m ' performs uniform circular motion of radius ' r ' with linear speed ' v ' under the application of force ' F '. If ' m ', ' v ' and ' \mathrm{r} ' are all increased by 20 \% the necessary change in force required to maintain the particle in uniform circular motion, is
Options:
A) 12 \%
B) 44 \%
C) 14 \%
D) 144 \%
229
EasyInteger TypeJEE Mains2025
In a hydraulic lift, the surface area of the input piston is 6 cm 2 and that of the output piston is 1500 cm 2 . If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is _______ kJ.
Answer: Enter a numeric value
230
MediumMHT CET2024
A particle rotates in a horizontal circle of radius 'R' in a conical funnel with constant speed 'V'. The inner surface of the funnel is smooth. The height of the plane of the circle from the vertex of the funnel is (g-acceleration due to gravity)
Options:
A) \frac{V}{g}
B) \frac{\mathrm{V}}{2 \mathrm{~g}}
C) \frac{\mathrm{V}^2}{2 \mathrm{~g}}
D) \frac{\mathrm{V}^2}{\mathrm{~g}}
231
MediumInteger TypeJEE Mains2025
A force \mathrm{f}=\mathrm{x}^2 \mathrm{y} \hat{\mathrm{i}}+\mathrm{y}^2 \hat{\mathrm{j}} acts on a particle in a plane \mathrm{x}+\mathrm{y}=10. The work done by this force during a displacement from (0,0) to (4 \mathrm{~m}, 2 \mathrm{~m}) is _________ Joule (round off to the nearest integer)
Answer: Enter a numeric value
232
MediumMHT CET2024
For a particle in uniform circular motion
Options:
A) linear velocity always radial to the circular path, without change in its magnitude
B) linear velocity always tangential to the circular path, without change in its magnitude
C) linear acceleration always tangential to the circular path
D) linear acceleration always along the axis of the circular path
233
EasyInteger TypeJEE Mains2024
A force $(3 x^2+2 x-5) \mathrm{N} displaces a body from x=2 \mathrm{~m} to x=4 \mathrm{~m}$. Work done by this force is ________ J.
Answer: Enter a numeric value
234
MediumMHT CET2024
A disc at rest is subjected to a uniform angular acceleration about its axis. Let \theta and \theta_1 be the angle made by the disc in 2^{\text {nd }} and 3^{\text {rd }} second of its motion. The ratio \frac{\theta}{\theta_1} is
Options:
A) 2: 3
B) 1: 2
C) 2: 3
D) 4: 5
235
EasyInteger TypeJEE Mains2023
A block of mass 10 \mathrm{~kg} is moving along \mathrm{x}-axis under the action of force F=5 x~ N. The work done by the force in moving the block from x=2 m to 4 m will be __________ J.
Answer: Enter a numeric value
236
MediumMHT CET2024
A body moves along a circular path of radius 15 cm . It starts from a point on the circular path and reaches the end of diameter in 3 second, The angular speed of the body in \mathrm{rad} / \mathrm{s} is
Options:
A) \frac{\pi}{2}
B) \frac{\pi}{3}
C) \frac{\pi}{4}
D) \frac{\pi}{5}
237
EasyInteger TypeJEE Mains2023
A car accelerates from rest to $u \mathrm{~m} / \mathrm{s}. The energy spent in this process is E J. The energy required to accelerate the car from u \mathrm{~m} / \mathrm{s} to 2 \mathrm{u} \mathrm{m} / \mathrm{s} is \mathrm{nE~J}. The value of \mathrm{n}$ is ____________.
Answer: Enter a numeric value
238
MediumMHT CET2024
A wheel of radius 1 m rolls through 180^{\circ} over a plane surface. The magnitude of the displacement of the point of the wheel initially in contact with the surface is.
Options:
A) 2 \pi
B) \pi
C) \sqrt{\pi^2+4}
D) 3 \pi
239
EasyInteger TypeJEE Mains2023
To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____________ KJ. [The coefficient of friction between tyre of bus and road is 0.04.]
Answer: Enter a numeric value
240
MediumMHT CET2024
The string of pendulum of length ' L ' is displaced through 90^{\circ} from the vertical and released. Then the maximum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is ( \mathrm{m}= mass of pendulum, \mathrm{g}= acceleration due to gravity)
Options:
A) mg
B) 3 mg
C) 5 mg
D) 6 mg
241
EasyInteger TypeJEE Mains2023
A block of mass $5 \mathrm{~kg} starting from rest pulled up on a smooth incline plane making an angle of 30^{\circ} with horizontal with an affective acceleration of 1 \mathrm{~ms}^{-2}. The power delivered by the pulling force at t=10 \mathrm{~s} from the start is ___________ W. [use \mathrm{g}=10 \mathrm{~ms}^{-2}$ ] (calculate the nearest integer value)
Answer: Enter a numeric value
242
MediumMHT CET2024
A particle at rest starts moving with a constant angular acceleration of 4 \mathrm{~rad} / \mathrm{s}^2 in a circular path. The time at which magnitudes of its centripetal acceleration and tangential acceleration will be equal, is (in second)
Options:
A) \frac{1}{4}
B) \frac{1}{3}
C) \frac{1}{2}
D) \frac{2}{3}
243
EasyInteger TypeJEE Mains2023
A force $\vec{F}=(2+3 x) \hat{i} acts on a particle in the x direction where F is in newton and x is in meter. The work done by this force during a displacement from x=0 to x=4 \mathrm{~m}$, is __________ J.
Answer: Enter a numeric value
244
MediumMHT CET2024
A particle is performing uniform circular motion along the circumference of the circle of diameter 1 m with frequency 4 Hz . The acceleration of the particle in \mathrm{m} / \mathrm{s}^2 is
Options:
A) 8 \pi^2
B) 16 \pi^2
C) 24 \pi^2
D) 32 \pi^2
245
EasyInteger TypeJEE Mains2023
If the maximum load carried by an elevator is $1400 \mathrm{~kg} ( 600 \mathrm{~kg} - Passengers + 800 \mathrm{kg} - elevator), which is moving up with a uniform speed of 3 \mathrm{~m} \mathrm{~s}^{-1} and the frictional force acting on it is 2000 \mathrm{~N}, then the maximum power used by the motor is __________ \mathrm{kW}\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)
Answer: Enter a numeric value
246
MediumMHT CET2023
A particle moves around a circular path of radius '$r' with uniform speed 'V$'. After moving half the circle, the average acceleration of the particle is
Options:
A) \frac{\mathrm{V}^2}{\mathrm{r}}
B) \frac{2 V^2}{r}
C) \frac{2 V^2}{\pi r}
D) \frac{\mathrm{V}^2}{\pi \mathrm{r}}
247
MediumInteger TypeJEE Mains2023
A closed circular tube of average radius 15 cm, whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fit inside the tube. The speed of block is 22 m/s, when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The work done by the tube on the block is __________ J. (Given g = 10 m/s$^2$).
Answer: Enter a numeric value
248
MediumMHT CET2023
On dry road, the maximum speed of a vehicle along a circular path is '$V'. When the road becomes wet, maximum speed becomes \frac{\mathrm{V}}{2}. If coefficient of friction of dry road is '\mu$' then that of wet road is
Options:
A) \frac{2 \mu}{3}
B) \frac{\mu}{4}
C) \frac{\mu}{3}
D) \frac{3 \mu}{4}
249
EasyInteger TypeJEE Mains2023
A body of mass $5 \mathrm{~kg} is moving with a momentum of 10 \mathrm{~kg} \mathrm{~ms}^{-1}. Now a force of 2 \mathrm{~N} acts on the body in the direction of its motion for 5 \mathrm{~s}. The increase in the Kinetic energy of the body is ___________ \mathrm{J}$.
Answer: Enter a numeric value
250
MediumMHT CET2023
A string of length '$L' fixed at one end carries a body of mass '\mathrm{m}' at the other end. The mass is revolved in a circle in the horizontal plane about a vertical axis passing through the fixed end of the string. The string makes angle '\theta' with the vertical. The angular frequency of the body is '\omega$'. The tension in the string is
Options:
A) \mathrm{mL}^2 \omega
B) \mathrm{mL} \omega^2
C) \frac{\omega^2}{\mathrm{~mL}}
D) \frac{\mathrm{m} \omega^2}{\mathrm{~L}}
251
EasyInteger TypeJEE Mains2023
A body is dropped on ground from a height '$h_{1}' and after hitting the ground, it rebounds to a height 'h_{2}'. If the ratio of velocities of the body just before and after hitting ground is 4 , then percentage loss in kinetic energy of the body is \frac{x}{4}. The value of x$ is ____________.
Answer: Enter a numeric value
252
MediumMHT CET2023
A stone is projected at angle $\theta with velocity u. If it executes nearly a circular motion at its maximum point for short time, then the radius of the circular path will be ( g=$ acceleration due to gravity)
Options:
A) \frac{u^2}{g}
B) \frac{u^2 \cos ^2 \theta}{g}
C) \frac{u^2 \sin ^2 \theta}{g}
D) \frac{u^2 \cos ^2 \theta}{2 g}
253
MediumInteger TypeJEE Mains2023
A particle of mass $10 \mathrm{~g} moves in a straight line with retardation 2 x, where x is the displacement in SI units. Its loss of kinetic energy for above displacement is \left(\frac{10}{x}\right)^{-n} J. The value of \mathrm{n}$ will be __________
Answer: Enter a numeric value
254
MediumMHT CET2023
A particle is moving in a circle with uniform speed '$v$'. In moving from a point to another diametrically opposite point
Options:
A) the momentum changes by $\mathrm{mv}
B) the momentum changes by $2 \mathrm{~mv}
C) the kinetic energy changes by $\frac{1}{2} \mathrm{mv}^2
D) the kinetic energy changes by $\mathrm{m v^2}
255
EasyInteger TypeJEE Mains2023
A block is fastened to a horizontal spring. The block is pulled to a distance $x=10 \mathrm{~cm} from its equilibrium position (at x=0) on a frictionless surface from rest. The energy of the block at x=5 \mathrm{cm} is 0.25 \mathrm{~J}. The spring constant of the spring is ___________ \mathrm{Nm}^{-1}
Answer: Enter a numeric value
256
MediumMHT CET2023
A body of mass '$\mathrm{m}' attached at the end of a string is just completing the loop in a vertical circle. The apparent weight of the body at the lowest point in its path is ( \mathrm{g}$ = gravitational acceleration)
Options:
A) zero
B) \mathrm{mg}
C) 3 \mathrm{~mg}
D) 6 \mathrm{~mg}
257
EasyInteger TypeJEE Mains2023
A force $\mathrm{F}=\left(5+3 y^{2}\right) acts on a particle in the y-direction, where \mathrm{F} is in newton and y is in meter. The work done by the force during a displacement from y=2 \mathrm{~m} to y=5 \mathrm{~m}$ is ___________ J.
Answer: Enter a numeric value
258
MediumMHT CET2023
A railway track is banked for a speed ',$v' by elevating outer rail by a height 'h' above the inner rail. The distance between two rails is 'd' then the radius of curvature of track is ( \mathrm{g}=$ gravitational acceleration)
Options:
A) \frac{\mathrm{v}^2 \mathrm{~d}}{\mathrm{gh}}
B) \mathrm{\frac{2 v^2}{g d h}}
C) \mathrm{\frac{g d}{2 v^2 h}}
D) \mathrm{\frac{v^2}{2 g h d}}
259
EasyInteger TypeJEE Mains2023
A small particle moves to position $5 \hat{i}-2 \hat{j}+\hat{k} from its initial position 2 \hat{i}+3 \hat{j}-4 \hat{k} under the action of force 5 \hat{i}+2 \hat{j}+7 \hat{k} \mathrm{~N}$. The value of work done will be __________ J.
Answer: Enter a numeric value
260
MediumMHT CET2023
Two particles having mass '$M' and 'm' are moving in a circular path with radius 'R' and 'r$' respectively. The time period for both the particles is same. The ratio of angular velocity of the first particle to the second particle will be
Options:
A) 1 : 1
B) 1 : 2
C) 2 : 3
D) 3 : 4
261
EasyInteger TypeJEE Mains2023
A lift of mass $\mathrm{M}=500 \mathrm{~kg} is descending with speed of 2 \mathrm{~ms}^{-1}. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of 2 \mathrm{~ms}^{-2}. The kinetic energy of the lift at the end of fall through to a distance of 6 \mathrm{~m} will be _____________ \mathrm{kJ}$.
Answer: Enter a numeric value
262
MediumMHT CET2023
In a conical pendulum the bob of mass '$\mathrm{m}' moves in a horizontal circle of radius 'r' with uniform speed '\mathrm{V}'. The string of length '\mathrm{L}' describes a cone of semi vertical angle '\theta'. The centripetal force acting on the bob is ( \mathrm{g}=$ acceleration due to gravity)
Options:
A) \frac{\mathrm{mgr}}{\sqrt{\mathrm{L}^2-\mathrm{r}^2}}
B) \frac{\mathrm{mgr}}{\left(\mathrm{L}^2-\mathrm{r}^2\right)}
C) \frac{\sqrt{\mathrm{L}^2-\mathrm{r}^2}}{\mathrm{mgL}}
D) \frac{\mathrm{mgL}}{\sqrt{\mathrm{L}^2-\mathrm{r}^2}}
263
MediumInteger TypeJEE Mains2023
A body of mass 2 \mathrm{~kg} is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in 4 \mathrm{~s} is \frac{1}{3} \alpha^{2} \sqrt{P} m. The value of \alpha will be ______.
Answer: Enter a numeric value
264
MediumMHT CET2023
A ball of mass '$\mathrm{m}' is attached to the free end of a string of length 'l'. The ball is moving in horizontal circular path about the vertical axis as shown in the diagram. The angular velocity '\omega' of the ball will be [ \mathrm{T}=$ Tension in the string.]
Options:
A) \sqrt{\frac{\mathrm{T} l}{\mathrm{~m}}}
B) \sqrt{\frac{\mathrm{Tm}}{l}}
C) \sqrt{\frac{\mathrm{m} l}{\mathrm{~T}}}
D) \sqrt{\frac{\mathrm{T}}{\mathrm{ml} l}}
265
MediumInteger TypeJEE Mains2023
A 0.4 kg mass takes 8s to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potential energy in the last second of fall is __________ J. (Take g = 10 m/s$^2$)
Answer: Enter a numeric value
266
MediumMHT CET2023
A particle performing uniform circular motion of radius $\frac{\pi}{2} \mathrm{~m} makes '\mathrm{x}' revolutions in time 't$'. Its tangential velocity is
Options:
A) \frac{\pi \mathrm{x}}{\mathrm{t}}
B) \frac{\pi x^2}{t}
C) \frac{\pi^2 x^2}{t}
D) \frac{\pi^2 \mathrm{x}}{\mathrm{t}}
267
MediumInteger TypeJEE Mains2023
An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N. In the process of its linear motion, the angle $\theta (as shown in figure) between the direction of force and horizontal varies as \theta=\mathrm{k}x, where k is a constant and x is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be E = {n \over k}\sin \theta $. The value of n is ___________.
Answer: Enter a numeric value
268
MediumMHT CET2023
A body of mass 200 gram is tied to a spring of spring constant $12.5 \mathrm{~N} / \mathrm{m}, while other end of spring is fixed at point 'O'. If the body moves about 'O' in a circular path on a smooth horizontal surface with constant angular speed 5 \mathrm{~rad} / \mathrm{s}$ then the ratio of extension in the spring to its natural length will be
Options:
A) 1 : 2
B) 1 : 1
C) 2 : 3
D) 2 : 5
269
MediumInteger TypeJEE Mains2023
A body of mass 1kg begins to move under the action of a time dependent force $\overrightarrow F = \left( {t\widehat i + 3{t^2}\,\widehat j} \right) N, where \widehat i and \widehat j are the unit vectors along x and y$ axis. The power developed by above force, at the time t = 2s, will be ____________ W.
Answer: Enter a numeric value
270
MediumMHT CET2023
A particle of mass '$\mathrm{m}' moves along a circle of radius 'r' with constant tangential acceleration. If K.E. of the particle is 'E$' by the end of third revolution after beginning of the motion, then magnitude of tangential acceleration is
Options:
A) \frac{\mathrm{E}}{2 \pi \mathrm{rm}}
B) \frac{\mathrm{E}}{6 \pi \mathrm{rm}}
C) \frac{\mathrm{E}}{8 \pi \mathrm{rm}}
D) \frac{\mathrm{E}}{4 \pi \mathrm{rm}}
271
EasyInteger TypeJEE Mains2023
A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of $\mathrm{5^{th}}$ second. The force acted on the body is ________ N.
Answer: Enter a numeric value
272
MediumMHT CET2023
A simple pendulum of length $2 \mathrm{~m} is given a horizontal push through angular displacement of 60^{\circ}. If the mass of bob is 200 gram, the angular velocity of the bob will be (Take Acceleration due to gravity =10 \mathrm{~m} / \mathrm{s}^2 ) \left(\sin 30^{\circ}=\cos 60^{\circ}=0.5, \cos 30^{\circ}=\sin 60^{\circ}=\sqrt{3} / 2\right)
Options:
A) 2 \sqrt{2} ~\mathrm{rad} / \mathrm{s}
B) 3 \sqrt{2} ~\mathrm{rad} / \mathrm{s}
C) 2 \sqrt{2.5} ~\mathrm{rad} / \mathrm{s}
D) 3 \sqrt{2.5} ~\mathrm{rad} / \mathrm{s}
273
MediumInteger TypeJEE Mains2022
A block of mass '$\mathrm{m}' (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 \mathrm{~cm} when, its speed is halved. The value of spring constant of used spring will be \mathrm{nE} \,\,\mathrm{Nm}^{-1} for \mathrm{n}=$ _________.
Answer: Enter a numeric value
274
MediumMHT CET2023
A particle at rest starts moving with constant angular acceleration $4 ~\mathrm{rad} / \mathrm{s}^2$ in circular path. At what time the magnitudes of its tangential acceleration and centrifugal acceleration will be equal?
Options:
A) 0.4 s
B) 0.5 s
C) 0.8 s
D) 1.0 s
275
EasyInteger TypeJEE Mains2022
A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is ___________ m.
Answer: Enter a numeric value
276
MediumMHT CET2022
A bucket containing water is revolved in a vertical circle of radius $r. To prevent the water from falling down, the minimum frequency of revolution required is (\mathrm{g}=$ acceleration due to gravity)
Options:
A) 2 \pi \sqrt{\frac{\mathrm{r}}{\mathrm{g}}}
B) \frac{1}{2 \pi} \sqrt{\frac{\mathrm{r}}{\mathrm{g}}}
C) \frac{1}{2 \pi} \sqrt{\frac{\mathrm{g}}{\mathrm{r}}}
D) 2 \pi \sqrt{\frac{\mathrm{g}}{\mathrm{r}}}
277
EasyInteger TypeJEE Mains2022
A 0.5 kg block moving at a speed of 12 ms $-1 compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be _______________ Nm -$1 .
Answer: Enter a numeric value
278
MediumMHT CET2022
A body moving in a circular path with a constant speed has constant
Options:
A) momentum
B) velocity
C) acceleration
D) kinetic energy
279
MediumInteger TypeJEE Mains2022
A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance ${h \over 2}. The spring constant is _____________ Nm -1 . (Use g = 10 ms -$2 )
Answer: Enter a numeric value
280
MediumMHT CET2022
Two bodies of masses '$\mathrm{m}' and '3 \mathrm{~m}' are rotating in horizontal speed of the body of mass 'm' is n times that of the value of heavier body; while the centripetal force is same for both. The value of n$ is
Options:
A) 3
B) 1
C) 9
D) 6
281
MediumInteger TypeJEE Mains2021
An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 40,000 kg is moving with a speed of 72 kmh $-1 when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of energy of the wagon is lost due to friction, the spring constant is ____________ \times$ 10 5 N/m.
Answer: Enter a numeric value
282
MediumMHT CET2021
A particle is moving along the circular path with constant speed and centripetal acceleration 'a'. If the speed is doubled, the ratio of its acceleration after and before the change is
Options:
A) 3: 1
B) 1: 4
C) 2: 1
D) 4: 1
283
MediumInteger TypeJEE Mains2021
A block moving horizontally on a smooth surface with a speed of 40 ms $-1 splits into two equal parts. If one of the parts moves at 60 ms -$1 in the same direction, then the fractional change in the kinetic energy will be x : 4 where x = ___________.
Answer: Enter a numeric value
284
MediumMHT CET2021
A body of mass 'm' is moving with speed 'V' along a circular path of radius 'r'. Now the speed is reduced to $\frac{V}{2}$ and radius is increased to '3r'. For this change, initial centripetal force needs to be
Options:
A) increased by $\frac{7}{12}$ times
B) increased by $\frac{10}{12}$ times
C) decreased by $\frac{11}{12}$ times
D) decreased by $\frac{1}{12}$ times
285
EasyInteger TypeJEE Mains2021
Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45$^\circ and 60^\circ with the direction of displacement respectively. The ratio of force applied by person A to the force applied by person B is {1 \over {\sqrt x }}$. The value of x is .................... .
Answer: Enter a numeric value
286
MediumMHT CET2021
A body attached to one end of a string performs motion along a vertical circle. Its centripetal acceleration, when the string is horizontal, will be [$\mathrm{g}=$ acceleration due to gravity]
Options:
A) zero
B) 5g
C) 3g
D) g
287
MediumInteger TypeJEE Mains2021
A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter lying on the table. If k is the kinetic energy of the chain in joule as it completely slips off the table, then the value of k is ................. . (Take g = 10 m/s 2 )
Answer: Enter a numeric value
288
MediumMHT CET2021
A projectile is thrown with an initial velocity $(a \hat{i}+b \hat{j}) \mathrm{m} / \mathrm{s}, where \hat{i} and \hat{j}$ are unit vectors along horizontal and vertical directions respectively. If the range of the projectile is twice the maximum height reached by it, then
Options:
A) \mathrm{b}=2 \mathrm{a}
B) \mathrm{b}=4 \mathrm{a}
C) \mathrm{b=\frac{a}{2}}
D) \mathrm{b}=\mathrm{a}
289
MediumInteger TypeJEE Mains2021
A small block slides down from the top of hemisphere of radius R = 3 m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is __________ m. (Assume there is no friction between the block and the hemisphere)
Answer: Enter a numeric value
290
MediumMHT CET2021
A particle is performing U.C.M. along the circumference of a circle of diameter $50 \mathrm{~cm} with frequency 2 \mathrm{~Hz}. The acceleration of the particle in \mathrm{m} / \mathrm{s}^2$ is
Options:
A) 2 \pi^2
B) 4 \pi^2
C) 8 \pi^2
D) \pi^2
291
EasyInteger TypeJEE Mains2021
A force of F = (5y + 20)$\widehat j$ N acts on a particle. The work done by this force when the particle is moved from y = 0 m to y = 10 m is ___________ J.
Answer: Enter a numeric value
292
MediumMHT CET2021
If $\omega_1 is angular velocity of hour hand of clock and \omega_2 is angular velocity of the earth, then the ratio \omega_1 : \omega_2$ is
Options:
A) 1 : 2
B) 2 : 3
C) 3 : 2
D) 2 : 1
293
MediumInteger TypeJEE Mains2021
In a spring gun having spring constant 100 N/m a small ball 'B' of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance 'd' on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground. The value of d is _________ m. (g = 10 m/s 2 ).
Answer: Enter a numeric value
294
MediumMHT CET2021
The angular displacement of body performing circular motion is given by $\theta=5 \sin \frac{\pi t}{6}. The angular velocity of the body at t=3 second will be \left[\sin \frac{\pi}{2}=1, \cos \frac{\pi}{2}=0\right]
Options:
A) 5 \frac{\mathrm{rad}}{\mathrm{s}}
B) 1 \frac{\mathrm{rad}}{\mathrm{s}}
C) 2.5 \frac{\mathrm{rad}}{\mathrm{s}}
D) zero $\frac{\mathrm{rad}}{\mathrm{s}}
295
EasyInteger TypeJEE Mains2021
A ball of mass 4 kg, moving with a velocity of 10 ms $-1 , collides with a spring of length 8 m and force constant 100 Nm -$1 . The length of the compressed spring is x m. The value of x, to the nearest integer, is ____________.
Answer: Enter a numeric value
296
MediumMHT CET2021
A body performing uniform circular motion of radius 'R' has frequency 'n'. It centripetal acceleration is
Options:
A) 8 $\pi^2nR^2
B) 4 $\pi^2n^2$R
C) 4 $\pi^2n^2R^2
D) 8 $\pi^2n^2$R
297
EasyInteger TypeJEE Mains2021
As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m/s. (Take g = 10 m/s 2 ) The value of 'x' to the nearest integer is __________.
Answer: Enter a numeric value
298
MediumMHT CET2021
The angle of banking '$\theta' for a meter gauge railway line is given by \theta=\tan ^{-1}\left(\frac{1}{20}\right)$. What is the elevation of the outer rail above the inner rail?
Options:
A) 20 \mathrm{~cm}
B) 10 \mathrm{~cm}
C) 0.2 \mathrm{~cm}
D) 5 \mathrm{~cm}
299
MediumInteger TypeJEE Mains2021
The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as $U = {\alpha \over {{r^{10}}}} - {\beta \over {{r^5}}} - 3 where, \alpha and \beta are positive constants. The equilibrium distance between two atoms will be {\left( {{{2\alpha } \over \beta }} \right)^{{a \over b}}}$, where a = ___________.
Answer: Enter a numeric value
300
MediumMHT CET2021
A particle moves in a circular orbit of radius '$r' under a central attractive force, F=-\frac{k}{r}, where \mathrm{k}$ is a constant. The periodic time of its motion is proportional to
Options:
A) r^{\frac{1}{2}}
B) \mathrm{r}^{\frac{2}{3}}
C) r
D) r^{\frac{3}{2}}
301
MediumInteger TypeJEE Mains2020
A body of mass 2 kg is driven by an engine delivering a constant power of 1 J/s. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) _______.
Answer: Enter a numeric value
302
MediumMHT CET2021
A particle at rest starts moving with a constant angular acceleration of $4 \mathrm{~rad} / \mathrm{s}^2$ in a circular path. At what time the magnitude of its centripetal acceleration and tangential acceleration will be equal?
Options:
A) \frac{1}{4} \mathrm{~S}
B) \frac{2}{3} \mathrm{~S}
C) \frac{1}{2} \mathrm{~S}
D) \frac{1}{3} \mathrm{~S}
303
MediumInteger TypeJEE Mains2020
A block starts moving up an inclined plane of inclination 30 o with an initial velocity of v 0 . It comes back to its initial position with velocity ${{{v_0}} \over 2}. The value of the coefficient of kinetic friction between the block and the inclined plane is close to {I \over {1000}}$. The nearest integer to I is____.
Answer: Enter a numeric value
304
MediumMHT CET2020
A child starts running from rest along a circular track of radius r with constant tangential acceleration a. After time t he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is [g = acceleration due to gravity]
Options:
A) \frac{\left[a^4 t^4+a^2 r^2\right]^{\frac{1}{2}}}{g r}
B) \frac{\left[a^4 t^4+a^2 r^2\right]}{r g}
C) \frac{\left[a^2 t^2+a^4 r^4\right]}{r g}
D) \frac{\left[a^4 t^4-a^2 r^2\right]^{\frac{1}{2}}}{r g}
305
MediumInteger TypeJEE Mains2020
A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force F on the ball and moves horizontally a distance of 0.2 m while launching the ball, the value of F (in N) is (g = 10 ms –2 ) ____.
Answer: Enter a numeric value
306
MediumMHT CET2020
A body is moving along a circular track of radius 100 m with velocity 20 \mathrm{~m} / \mathrm{s}. Its tangential acceleration is 3 \mathrm{~m} / \mathrm{s}^2, then its resultant acceleration will be
Options:
A) 5 \mathrm{~m} / \mathrm{s}^2
B) 4 \mathrm{~m} / \mathrm{s}^2
C) 2 \mathrm{~m} / \mathrm{s}^2
D) 3 \mathrm{~m} / \mathrm{s}^2
307
MediumInteger TypeJEE Mains2020
A small block starts slipping down from a point B on an inclined plane AB, which is making an angle $\theta with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction \mu . It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2AC, the coefficient of friction is given by \mu = ktan \theta $ . The value of k is _________.
Answer: Enter a numeric value
308
MediumMHT CET2020
A particle starting from rest moves along the circumference of a circle of radius $r with angular acceleration \alpha. The magnitude of the average velocity, in the time it completes the small angular displacement \theta$ is
Options:
A) r\left(\frac{2}{\alpha \theta}\right)^2
B) r\left(\frac{\alpha \theta}{2}\right)^2
C) \rho\left(\frac{\alpha \theta}{2}\right)
D) r\left(\frac{\alpha \theta}{2}\right)^{\frac{1}{2}}
309
MediumInteger TypeJEE Mains2020
A particle (m = 1 kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reaching its highest point P (height 1 m), the kinetic energy of the particle (in )) is : (Figure drawn is schematic and not to scale; take g = 10 ms -2 )
Answer: Enter a numeric value
310
MediumMHT CET2020
A particle of mass $m is performing UCM along a circle of radius r. The relation between centripetal acceleration a and kinetic energy E$ is given by
Options:
A) a=\frac{2 E}{m r}
B) a=2 E m
C) a=\frac{E}{m r}
D) a=\left(\frac{2 E}{m r}\right)^2
311
HardJEE Advanced2020
A student skates up a ramp that makes an angle 30$^\circ$ with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed v 0 and wants to turn around over a semicircular path xyz of radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)
Options:
A) v_0^2 - 2gh = {1 \over 2}gR
B) v_0^2 - 2gh = {{\sqrt 3 } \over 2}gR
C) the centripetal force required at points x and z is zero
D) the centripetal force required is maximum at points x and z
312
MediumMHT CET2020
In non-uniform circular motion, the ratio of tangential to radial acceleration is ($r= radius, \alpha= angular acceleration and v=$ linear velocity)
Options:
A) \frac{r \alpha}{v}
B) \frac{v^2}{r a}
C) \frac{r \alpha^2}{v^2}
D) \frac{r^2 \alpha}{v^2}
313
MediumJEE Advanced2019
A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is L = L 0 , the particle speed is v = v 0 . The piston is moved inward at a very low speed V such that $V < < {{dL} \over L}{v_0}$, where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?
Options:
A) After each collision with the piston, the particle speed increases by 2V.
B) If the piston moved inward by dL, the particle speed increases $2v{{dL} \over L}$.
C) The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from L
0
to 1/2 L
0
.
D) The rate at which the particle strikes the piston is v/L.
314
MediumMHT CET2020
A particle is moving in a radius $R with constant speed v$. The magnitude of average acceleration after half revolution is
Options:
A) \frac{2 \pi}{R v^2}
B) \frac{2 R}{\pi v}
C) \frac{2 v^2}{\pi R}
D) \frac{2 V}{\pi R^2}
315
HardJEE Advanced2018
A particle of mass $m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as dK/dt = \gamma t, where \gamma $ is a positive constant of appropriate dimensions. Which of a positive constant of appropriate dimensions. Which of the following statement is (are) true?
Options:
A) The force applied on the particle is constant
B) The speed of the particle is proportional to time
C) The distance of the particle from the origin increases linearly with time
D) The force is conservative
316
MediumMHT CET2019
A mass is whirled in a circular path with constant angular velocity and its linear velocity is v. If the string is now halved keeping the angular momentum same, the linear velocity is
Options:
A) 2 v
B) \frac{v}{2}
C) v
D) v \sqrt{2}
317
HardJEE Advanced2017
A flat plate is moving normal to its plane through a gas under the reaction of a constant force $F. The gas is kept at a very low pressure. The speed of the plate v$ is much less than the average speed u of the gas molecules. Which of the following options is /are true?
Options:
A) The pressure difference between the leading and trailing faces of the plate is proportional to uv
B) The resistive force experimenced by the plate is proportional to $v
C) The plate will continue to move with constant non-zero acceleration, at all times
D) At a later time the external force $F$ balances the resistive force
318
MediumMHT CET2019
A body of mass m is performing a UCM in a circle of radius r with speed v. The work done by the centripetal force in moving it through \left(\frac{2}{3}\right) \mathrm{rd} of the circular path is
Options:
A) zero
B) m v^2 \pi r
C) \frac{2 \pi m v^2 r}{3}
D) \frac{2 m v^2 \pi}{3}
319
HardJEE Advanced2011
A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision,
Options:
A) the ring has pure rotation about its stationary CM.
B) the ring comes to a complete stop.
C) friction between the ring and the ground is to the left.
D) there is no friction between the ring and the ground.
320
MediumMHT CET2019
In U.C.M., when time interval \delta t \rightarrow 0, the angle between change in velocity ( \delta \mathbf{v} ) and linear velocity (\boldsymbol{v}) will be
Options:
A) 0^\circ
B) 90^\circ
C) 180^\circ
D) 45^\circ
321
MediumJEE Advanced2006
A ball moves over a fixed track as shown in the figure. From A to B, the ball rolls without slipping. Surface B C is frictionless. K_A, K_B and K_c are kinetic energies of the ball at A, B and C , respectively. Then
Options:
A) h_{\mathrm{A}}>h_{\mathrm{c}^{\prime}} \mathrm{K}_{\mathrm{B}}>\mathrm{K}_{\mathrm{C}}.
B) h_{\mathrm{A}}>h_{\mathrm{c}} ; \mathrm{K}_{\mathrm{C}}>\mathrm{K}_{\mathrm{A}}.
C) h_{\mathrm{A}}=h_{\mathrm{c}} ; \mathrm{K}_{\mathrm{B}}=\mathrm{K}_{\mathrm{C}}.
D) h_{\mathrm{A}} < h_{\mathrm{c}} ; \mathrm{K}_{\mathrm{B}}>\mathrm{K}_{\mathrm{C}}.
322
MediumMHT CET2019
A particle is performing U.C.M. along the circumference of a circle of diameter 50 cm with frequency 2 Hz . The acceleration of the particle in \mathrm{m} / \mathrm{s}^2 is
Options:
A) 2 \pi^2
B) 8 \pi^2
C) \pi^2
D) 4 \pi^2
323
MediumJEE AdvancedIIT-JEE 1998 Screening
A force $F = - K\left( {y\widehat i + x\widehat j} \right) (where K is a positive constant) acts on a particle moving in the xy plane. Starting from the origin, the particle is taken along the positive x axis to the point \left( {a,0} \right), and then parallel to the y axis to the point \left( {a,a} \right)$. The total work done by the force F on the particle is
Options:
A) - 2K{a^2}
B) 2K{a^2}
C) - K{a^2}
D) K{a^2}
324
MediumMHT CET2019
A stone of mass 1 kg is tied to a string 2 m long and it's rotated at constant speed of 40 \mathrm{~ms}^{-1} in a vertical circle. The ratio of the tension at the top and the bottom is [Take g=10 \mathrm{~ms}^{-2}]
Options:
A) \frac{81}{79}
B) \frac{79}{81}
C) \frac{19}{12}
D) \frac{12}{19}
325
MediumJEE AdvancedIIT-JEE 1998 Screening
A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the center. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is
Options:
A) \sqrt {{u^2} - 2gL}
B) \sqrt {2gL}
C) \sqrt {{u^2} - gL}
D) \sqrt {2\left( {{u^2} - gL} \right)}
326
MediumMHT CET2019
The real force ' F ' acting on a particle of mass m ' performing circular motion acts along the radius of circle ' r ' and is directed towards the centre of circle. The square root of magnitude of such force is ( T= periodic time)
Options:
A) \frac{2 \pi}{T} \sqrt{m r}
B) \frac{T m r}{4 \pi}
C) \frac{2 \pi T}{\sqrt{m r}}
D) \frac{T^2 m r}{4 \pi}
327
MediumJEE AdvancedIIT-JEE 1987
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that :
Options:
A) Its velocity is constant
B) its acceleration is constant
C) its kinetic energy is constant
D) it moves in a circular path
328
MediumVITEEE2025
A ball suspended by a thread swings in a vertical plane, so that its acceleration in the extreme position and lowest position are equal. The angle \theta of thread deflection in the extreme position will be
Options:
A) \tan ^{-1}(2)
B) \tan ^{-1}(\sqrt{2})
C) \tan ^{-1}\left(\frac{1}{2}\right)
D) 2 \tan ^{-1}\left(\frac{1}{2}\right)
329
MediumJEE AdvancedIIT-JEE 1985
A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is
Options:
A) MgL
B) {{MgL} \over 3}
C) {{MgL} \over 9}
D) {{MgL} \over {18}}
330
MediumVITEEE2022
A cone filled with water is revolved in a vertical circle of radius $4 \mathrm{~m}$ and the water does not fall down. What must be the maximum period of revolution?
Options:
A) 2s
B) 4s
C) 1s
D) 6s
331
MediumJEE AdvancedIIT-JEE 1984
A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in the time t is proportional to
Options:
A) t
1/2
B) t
3/4
C) t
3/2
D) t
2
332
MediumVITEEE2022
A train has to negotiate a curve of radius $400 \mathrm{~m}. By how much should the outer rail be raised with respect to the inner rail for a speed of 48 \mathrm{~km} / \mathrm{h} ? The distance between the rails is 1 \mathrm{~m}$.
Options:
A) 1.5 cm
B) 2.5 cm
C) 3.5 cm
D) 4.5 cm
333
MediumInteger TypeJEE Advanced2019
A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force $F = (\alpha y\widehat i + 2\alpha x\widehat j) N, where x and y are in meter and \alpha = - $1 Nm -1 . The work done on the particle by this force F will be ............... Joule.
Answer: Enter a numeric value
334
MediumInteger TypeJEE Advanced2018
A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0\,N{m^{ - 1}} and the mass of the block is 2.0 kg. Ignore the mass of the spring. Initially the spring is an unstretched condition. Another block of mass 1.0 kg moving with a speed of 2.0 m{s^{ - 1}} collides elastically with the first block. The collision is such that the 2.0 kg$ block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is __________.
Answer: Enter a numeric value
335
MediumInteger TypeJEE Advanced2014
Consider an elliptically shaped rail PQ in the vertical plane with OP = 3 m and OQ = 4 m. A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is (n × 10) Joules. The value of n is (take acceleration due to gravity = 10 ms –2 )
Answer: Enter a numeric value
336
MediumInteger TypeJEE Advanced2013
A bob of mass m, suspended by a string of length l 1 is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l 2 , which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio ${{{l_1}} \over {{l_2}}}$ is
Answer: Enter a numeric value
337
MediumInteger TypeJEE Advanced2013
A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in m/s) of the particle is zero, the speed (in m/s) after 5 s is
Answer: Enter a numeric value
338
MediumInteger TypeJEE Advanced2011
A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is
Answer: Enter a numeric value
339
MediumInteger TypeJEE Advanced2009
A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s 2 , find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.
Answer: Enter a numeric value
340
MediumInteger TypeJEE Advanced2009
Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C.
Answer: Enter a numeric value
341
MediumInteger TypeJEE Advanced2006
There is a rectangular plate of mass M kg of dimensions ( a \times b ). The plate is held in horizontal position by striking n small balls each of mass m per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity v. What is v ? It is given n=100, \mathrm{M}=3 \mathrm{~kg}, m=0.01 \mathrm{~kg}; b=2 m ; a=1 \mathrm{~m} ; g=10 \mathrm{~m} / \mathrm{s}^2
Answer: Enter a numeric value
342
HardJEE Advanced2018
In the List-${\rm I} below, four different paths of a particle are given as functions of time. In these functions, \alpha and \beta are positive constants of appropriate dimensions and \alpha \ne \beta In each case, the force acting on the particle is either zero or conservative. In List-{\rm I}{\rm I}, five physical quantities of the particle are mentioned \overrightarrow p is the linear momentum, \overrightarrow L is the angular momentum about the origin, K is the kinetic energy, U is the potential energy and E is the total energy. Match each path in List-{\rm I} with those quantities in List-{\rm II}, which are conserved for that path. LIST - I LIST - II P. \overrightarrow r (t)=\alpha t\,\widehat i + \beta t\widehat j 1. \overrightarrow p Q. \overrightarrow r \left( t \right) = \alpha \cos \,\omega t\,\widehat i + \beta \sin \omega t\,\widehat j 2. \overrightarrow L R. \overrightarrow r \left( t \right) = \alpha \left( {\cos \omega t\,\widehat i + \sin \omega t\widehat j} \right) 3. K S. \overrightarrow r \left( t \right) = \alpha t\,\widehat i + {\beta \over 2}{t^2}\widehat j$ 4. U 5. E
Options:
A) P \to 1,2,3,4,5;\,Q \to 2,5;R \to 2,3,4,5;S \to 5
B) P \to 1,2,3,4,5;{\mkern 1mu} Q \to 3,5;R \to 2,3,4,5;S \to 2,5
C) P \to 2,3,4;{\mkern 1mu} Q \to 5;R \to 1,2,4;S \to 2,5
D) P \to 1,2,3,4,5;{\mkern 1mu} Q \to 2,5;R \to 2,3,4,5;S \to 2,5
343
HardJEE Advanced2015
A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in Column I (a and U 0 are constants). Match the potential energies in Column I to the corresponding statement(s) in Column II:
Options:
A) (A)→(P), (Q), (R); (B)→(Q), (S); (C)→(P), (Q), (R), (S); (D)→(P), (R), (T)
B) (A)→(P), (Q), (R), (T); (B)→(Q), (S); (C)→(P), (Q), (R), (S); (D)→(P), (R), (T)
C) (A)→(P), (Q), (R), (T); (B)→(Q); (C)→(P), (Q), (R), (S); (D)→(P), (R), (T)
D) (A)→(P), (Q), (R), (T); (B)→(Q), (S); (C)→(P), (Q), (R), (S); (D)→(P), (R)
344
MediumJEE Advanced2014
A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy K with time t most appropriately? The figures are only illustrative and not to the scale.
Options:
A)
B)
C)
D)
345
MediumJEE Advanced2013
A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, below, is 150 J. (Take the acceleration due to gravity, g = 10 m/s 2 )
Options:
A) 7.5 N
B) 8.6 N
C) 11.5 N
D) 22.5 N
346
MediumJEE Advanced2013
A small block of mass 1 kg is released from rest at the top of a rough track. The track is circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, below, is 150 J. (Take the acceleration due to gravity, g = 10 m/s 2 )
Options:
A) 5 ms
-1
B) 10 ms
-1
C) 10\sqrt 3 $ ms
-1
D) 20 ms
-1
347
MediumJEE Advanced2013
The work done on a particle of mass m by a force $$K\left[ {{x \over {{{\left( {{x^2} + {y^2}} \right)}^{3/2}}}}\widehat i + {y \over {{{\left( {{x^2} + {y^2}} \right)}^{3/2}}}}\widehat j} \right] (K being a constant of appropriate dimensions), when the particle is taken from the point \left( {a,0} \right) to the point \left( {0,a} \right)$ along a circular path of radius a about the origin in the x-y plane is
Options:
A) {{2K\pi } \over a}
B) {{K\pi } \over a}
C) {{K\pi } \over {2a}}
D) 0
348
MediumJEE Advanced2010
A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards, it is subjected to a time-dependent force F(t) in the x-direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 s is
Options:
A) 4.50 J
B) 7.50 J
C) 5.06 J
D) 14.06 J
349
HardJEE Advanced2008
A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio $\frac{y}{x}$ is :
Options:
A) 4
B) 2
C) \frac{1}{2}
D) \frac{1}{4}
350
MediumJEE Advanced2008
A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle $\theta$ at which the speed of the bob is half of that at A, satisfies,
Options:
A) \theta = {\pi \over 4}
B) {\pi \over 4} < \theta < {\pi \over 2}
C) {\pi \over 2} < \theta < {{3\pi } \over 4}
D) {{3\pi } \over 4} < \theta < \pi
351
MediumJEE Advanced2007
Statement 1 : A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30$^\circ$ with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. Statement 2 : The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.
Options:
A) Statement 1 is True, Statement 2 is True, Statement 2 is a CORRECT explanation for Statement 1
B) Statement 1 is True, Statement 2 is True, Statement 2 is NOT a CORRECT explanation for Statement 1
C) Statement 1 is True, Statement 2 is False
D) Statement 1 is False, Statement 2 is True
352
MediumJEE Advanced2004
A particle is acted by a force F = kx, where k is a +ve constant. Its potential energy at x = 0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x
Options:
A)
B)
C)
D)
353
MediumJEE Advanced2003
If W 1 , W 2 and W 3 represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W 1 , W 2 and W 3 .
Options:
A) W1 > W2 > W3
B) W1 = W2 = W3
C) W1 < W2 < W3
D) W2 > W1 > W3
354
MediumJEE Advanced2002
An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is
Options:
A) {{4Mg} \over k}
B) {{2Mg} \over k}
C) {{Mg} \over k}
D) {{Mg} \over {2k}}
355
MediumJEE Advanced2000
A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to
Options:
A) v
B) v
2
C) v
3
D) v
4
356
MediumJEE AdvancedIIT-JEE 1999 Screening
A spring of force-constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force-constant of
Options:
A) \left( {{2 \over 3}} \right)k
B) \left( {{3 \over 2}} \right)k
C) 3 k
D) 6 k
357
MediumJEE AdvancedIIT-JEE 1994
A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ${a_c} is varying with time t as {a_c}$ = k 2 rt 2 where k is a constant. The power delivered to the perticles by the force acting on it is:
Options:
A) 2\pi m{k^2}{r^2}t
B) m{k^2}{r^2}t
C) {{\left( {m{k^4}{r^2}{t^5}} \right)} \over 3}
D) zero
358
MediumJEE AdvancedIIT-JEE 1980
If a machine is lubricated with oil
Options:
A) the mechanical advantage of the machine increases
B) the mechanical efficiency of the machine increases
C) both its mechanical advantage and efficiency increases
D) its efficiency increases, but its mechanical advantage decreases
359
MediumJEE AdvancedIIT-JEE 1980
Two masses of 1gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is
Options:
A) 4 : 1
B) \sqrt 2 :1
C) 1:2
D) 1 : 16
359
Total Questions
74
Easy
271
Medium
14
Hard
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