Class 11 • Physics

Properties of Matter

Chapter-8

453 Questions

0 Video Solutions

119 Easy326 Medium8 Hard

Practice Questions

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D) 278 kPa

EasyJEE Mains2023

Match List I with List II List I List II A. Surface tension I. $\mathrm{kg~m^{-1}~s^{-1}} B. Pressure II. \mathrm{kg~ms^{-1}} C. Viscosity III. \mathrm{kg~m^{-1}~s^{-2}} D. Impulse IV. \mathrm{kg~s^{-2}}$ Choose the correct answer from the options given below :

Options:

A) A-IV, B-III, C-I, D-II

B) A-IV, B-III, C-II, D-I

C) A-I, B-I, C-III, D-IV

D) A-III, B-IV, C-I, D-II

100

EasyJEE Mains2023

A bowl filled with very hot soup cools from 98$^\circC to 86^\circC in 2 minutes when the room temperature is 22^\circC. How long it will take to cool from 75^\circC to 69^\circ$C?

Options:

A) 2 minutes

B) 0.5 minute

C) 1.4 minutes

D) 1 minute

101

EasyJEE Mains2023

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Steel is used in the construction of buildings and bridges. Reason R : Steel is more elastic and its elastic limit is high. In the light of above statements, choose the most appropriate answer from the options given below

Options:

A) Both A and R are correct and R is the correct explanation of A

B) A is correct but R is not correct

C) Both A and R are correct but R is NOT the correct explanation of A

D) A is not correct but R is correct

102

MediumJEE Mains2023

The frequency ($\nu) of an oscillating liquid drop may depend upon radius (r) of the drop, density (\rho) of liquid and the surface tension (s) of the liquid as \nu=r^a\rho^b s^c$. The values of a, b and c respectively are

Options:

A) \left( {{3 \over 2},{1 \over 2}, - {1 \over 2}} \right)

B) \left( { - {3 \over 2}, - {1 \over 2},{1 \over 2}} \right)

C) \left( {{3 \over 2}, - {1 \over 2},{1 \over 2}} \right)

D) \left( { - {3 \over 2},{1 \over 2},{1 \over 2}} \right)

103

EasyJEE Mains2023

A 100 m long wire having cross-sectional area $\mathrm{6.25\times10^{-4}~m^2} and Young's modulus is \mathrm{10^{10}~Nm^{-2}}$ is subjected to a load of 250 N, then the elongation in the wire will be :

Options:

A) \mathrm{6.25\times10^{-6}~m}

B) \mathrm{4\times10^{-3}~m}

C) \mathrm{4\times10^{-4}~m}

D) \mathrm{6.25\times10^{-3}~m}

104

EasyJEE Mains2022

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash. Reason (R): Because the angle of contact between the oil/grease and water is obtuse. In the light of the above statements, choose the correct answer from the option given below.

Options:

A) Both (A) and (R) are true and (R) is the correct explanation of (A)

B) Both (A) and (R) are true but (R) is not the correct explanation of (A)

C) (A) is true but (R) is false

D) (A) is false but (R) is true

105

EasyJEE Mains2022

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :

Options:

A) remain same

B) become 8 times its initial value

C) become $\frac{1}{4}$ of its initial value

D) become 4 times its initial value

106

EasyJEE Mains2022

A pressure-pump has a horizontal tube of cross sectional area $10 \mathrm{~cm}^{2} for the outflow of water at a speed of 20 \mathrm{~m} / \mathrm{s}. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is : [given: density of water =1000 \mathrm{~kg} / \mathrm{m}^{3}$]

Options:

A) 300 N

B) 500 N

C) 250 N

D) 400 N

107

MediumJEE Mains2022

Consider a cylindrical tank of radius $1 \mathrm{~m} is filled with water. The top surface of water is at 15 \mathrm{~m} from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 \mathrm{~m} from the bottom. A force of 5 \times 10^{5} \mathrm{~N} is applied an the top surface of water using a piston. The speed of ifflux from the hole will be : (given atmospheric pressure \mathrm{P}_{\mathrm{A}}=1.01 \times 10^{5} \mathrm{~Pa}, density of water \rho_{\mathrm{W}}=1000 \mathrm{~kg} / \mathrm{m}^{3} and gravitational acceleration \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ )

Options:

A) 11.6 m/s

B) 10.8 m/s

C) 17.8 m/s

D) 14.4 m/s

108

EasyJEE Mains2022

A balloon has mass of $10 \mathrm{~g} in air. The air escapes from the balloon at a uniform rate with velocity 4.5 \mathrm{~cm} / \mathrm{s}. If the balloon shrinks in 5 \mathrm{~s}$ completely. Then, the average force acting on that balloon will be (in dyne).

Options:

A) 3

B) 9

C) 12

D) 18

109

EasyJEE Mains2022

The force required to stretch a wire of cross-section $1 \mathrm{~cm}^{2} to double its length will be : (Given Yong's modulus of the wire =2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$)

Options:

A) 1 \times 10^{7} \mathrm{~N}

B) 1.5 \times 10^{7} \mathrm{~N}

C) 2 \times 10^{7} \mathrm{~N}

D) 2.5 \times 10^{7} \mathrm{~N}

110

EasyJEE Mains2022

A steel wire of length $3.2 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{s}}=2.0 \times 10^{11} \,\mathrm{Nm}^{-2}\right) and a copper wire of length 4.4 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{c}}=1.1 \times 10^{11} \,\mathrm{Nm}^{-2}\right), both of radius 1.4 \mathrm{~mm} are connected end to end. When stretched by a load, the net elongation is found to be 1.4 \mathrm{~mm}. The load applied, in Newton, will be: \quad\left(\right. Given \pi=\frac{22}{7}$)

Options:

A) 360

B) 180

C) 1080

D) 154

111

MediumJEE Mains2022

Two cylindrical vessels of equal cross-sectional area $16 \mathrm{~cm}^{2} contain water upto heights 100 \mathrm{~cm} and 150 \mathrm{~cm} respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take, density of water =10^{3} \mathrm{~kg} / \mathrm{m}^{3} and \mathrm{g}=10 \mathrm{~ms}^{-2}$ ] :

Options:

A) 0.25 J

B) 1 J

C) 8 J

D) 12 J

112

EasyJEE Mains2022

The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} \mathrm{~m}^{2}. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be : (take g=10 \,m s^{-2}$ )

Options:

A) 6.25\times 10^{-4} \mathrm{~m}^{2}

B) 10\times 10^{-4} \mathrm{~m}^{2}

C) 1\times 10^{-4} \mathrm{~m}^{2}

D) 1.67\times 10^{-4} \mathrm{~m}^{2}

113

MediumJEE Mains2022

A water drop of radius $1 \mathrm{~cm} is broken into 729 equal droplets. If surface tension of water is 75 dyne/ \mathrm{cm}, then the gain in surface energy upto first decimal place will be : (Given \pi=3.14$ )

Options:

A) 8.5 \times 10^{-4} \mathrm{~J}

B) 8.2 \times 10^{-4} \mathrm{~J}

C) 7.5 \times 10^{-4} \mathrm{~J}

D) 5.3 \times 10^{-4} \mathrm{~J}

114

MediumJEE Mains2022

A drop of liquid of density $\rho is floating half immersed in a liquid of density {\sigma} and surface tension 7.5 \times 10^{-4} Ncm -1 . The radius of drop in \mathrm{cm} will be : (g = 10 ms -$2 )

Options:

A) \frac{15}{\sqrt{(2 \rho-\sigma)}}

B) \frac{15}{\sqrt{(\rho-\sigma)}}

C) \frac{3}{2 \sqrt{(\rho-\sigma)}}

D) \frac{3}{20 \sqrt{(2 \rho-\sigma)}}

115

MediumJEE Mains2022

An air bubble of negligible weight having radius r rises steadily through a solution of density $\sigma$ at speed v. The coefficient of viscosity of the solution is given by :

Options:

A) \eta = {{4r\sigma g} \over {9v}}

B) \eta = {{2{r^2}\sigma g} \over {9v}}

C) \eta = {{2\pi {r^2}\sigma g} \over {9v}}

D) \eta = {{2{r^2}\sigma g} \over {3\pi v}}

116

MediumJEE Mains2022

A wire of length L is hanging from a fixed support. The length changes to L 1 and L 2 when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to :

Options:

A) \sqrt {{L_1}{L_2}}

B) {{{L_1} + {L_2}} \over 2}

C) 2{L_1} - {L_2}

D) 3{L_1} - 2{L_2}

117

MediumJEE Mains2022

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs $-1 and at a speed of 10 ms -1 . Then, the initial acceleration of the block, in ms -$2 , will be :

Options:

A) 3

B) 6

C) 5

D) 4

118

EasyJEE Mains2022

A water drop of radius 1 $\mum falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1.8 \times 10 -5 Nsm -2 and its density is negligible as compared to that of water 10 6 gm -3 . Terminal velocity of the water drop is : (Take acceleration due to gravity = 10 ms -$2 )

Options:

A) 145.4 $\times 10 -6 ms -$1

B) 118.0 $\times 10 -6 ms -$1

C) 132.6 $\times 10 -6 ms -$1

D) 123.4 $\times 10 -6 ms -$1

119

EasyJEE Mains2022

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity. Reason R : Coefficient of viscosity = ${{Force} \over {Velocity\,gradient}}$ Choose the correct answer from the options given below :

Options:

A) Both A and R are true, and R is the correct explanation of A.

B) Both A and R are true but R is NOT the correct explanation of A.

C) A is true but R is false.

D) A is false but R is true.

120

MediumJEE Mains2022

A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be :

Options:

A) 2.8 $\times 10 -$4 J

B) 1.5 $\times 10 -$3 J

C) 1.9 $\times 10 -$4 J

D) 9.4 $\times 10 -$5 J

121

EasyJEE Mains2022

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

Options:

A) 19.6 m

B) 29.4 m

C) 39.2 m

D) 73.5 m

122

EasyJEE Mains2022

The velocity of a small ball of mass 'm' and density d 1 , when dropped in a container filled with glycerin, becomes constant after some time. If the density of glycerin is d 2 , then the viscous force acting on the ball, will be :

Options:

A) mg\left( {1 - {{{d_1}} \over {{d_2}}}} \right)

B) mg\left( {1 - {{{d_2}} \over {{d_1}}}} \right)

C) mg\left( {{{{d_1}} \over {{d_2}}} - 1} \right)

D) mg\left( {{{{d_2}} \over {{d_1}}} - 1} \right)

123

EasyJEE Mains2022

If p is the density and $\eta$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number R e is :

Options:

A) {R_e} = {{\eta d} \over {\rho v}}

B) {R_e} = {{\rho v} \over {\eta d}}

C) {R_e} = {{\rho vd} \over \eta }

D) {R_e} = {\eta \over {\rho vd}}

124

EasyJEE Mains2022

The terminal velocity (v t ) of the spherical rain drop depends on the radius (r) of the spherical rain drop as :

Options:

A) r 1/2

B) r

C) r 2

D) r 3

125

EasyJEE Mains2022

Potential energy as a function of r is given by $U = {A \over {{r^{10}}}} - {B \over {{r^5}}}$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

Options:

A) {\left( {{A \over B}} \right)^{{1 \over 5}}}

B) {\left( {{B \over A}} \right)^{{1 \over 5}}}

C) {\left( {{2A \over B}} \right)^{{1 \over 5}}}

D) {\left( {{B \over 2A}} \right)^{{1 \over 5}}}

126

EasyJEE Mains2022

The bulk modulus of a liquid is 3 $\times 10 10 Nm -$2 . The pressure required to reduce the volume of liquid by 2% is :

Options:

A) 3 $\times 10 8 Nm -$2

B) 9 $\times 10 8 Nm -$2

C) 6 $\times 10 8 Nm -$2

D) 12 $\times 10 8 Nm -$2

127

EasyJEE Mains2021

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 $\times 10 3 kg. The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use Y = 2.0 \times$ 10 11 Pa, g = 9.8 m/s 2 ]

Options:

A) 3.60 $\times 10 -$8

B) 2.60 $\times 10 -$7

C) 1.87 $\times 10 -$3

D) 7.07 $\times 10 -$4

128

EasyJEE Mains2021

A uniform heavy rod of weight 10 kg ms $-2 , cross-sectional area 100 cm 2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 \times 10 11 Nm -$2 . Neglecting the lateral contraction, find the elongation of rod due to its own weight.

Options:

A) 2 $\times 10 -$9 m

B) 5 $\times 10 -$8 m

C) 4 $\times 10 -$8 m

D) 5 $\times 10 -$10 m

129

EasyJEE Mains2021

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2.0 $\times 10 -5 m and density 1.2 \times 10 3 kgm -3 ? Take viscosity of liquid = 1.8 \times 10 -5 Nsm -$2 . (Neglect buoyancy due to air).

Options:

A) 3.8 $\times 10 -$11 N

B) 3.9 $\times 10 -$10 N

C) 1.8 $\times 10 -$10 N

D) 5.8 $\times 10 -$10 N

130

MediumJEE Mains2021

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is ${{24} \over \pi } \times {10^2}$ Nm -2 . What is the minimum radius of the wire ? (Take g = 10 ms -2 )

Options:

A) 125 cm

B) 1250 cm

C) 12.5 cm

D) 1.25 cm

131

MediumJEE Mains2021

Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7.3 $\times 10 -2 Nm -1 , angle of contact = 0, g = 10 ms 2 and density of water = 1.0 \times 10 3 kg m -$3 ]

Options:

A) 3.62 mm

B) 2.19 mm

C) 5.34 mm

D) 4.97 mm

132

MediumJEE Mains2021

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is : [Density of water f w = 1000 kg m $-3 and Density of air f a = 1.2 kg m -3 , g = 10 m/s 2 , Coefficient of viscosity of air = 1.8 \times 10 -5 Nsm -$2 ]

Options:

A) 250.6 ms $-$1

B) 43.56 ms $-$1

C) 4.94 ms $-$1

D) 14.4 ms $-$1

133

MediumJEE Mains2021

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a < < A) :

Options:

A) {A \over {2a}}

B) None of these

C) {{2a} \over A}

D) {{a} \over A}

134

EasyJEE Mains2021

A body takes 4 min. to cool from 61$^\circ C to 59^\circ C. If the temperature of the surroundings is 30^\circ C, the time taken by the body to cool from 51^\circ C to 49^\circ$ C is :

Options:

A) 4 min.

B) 3 min.

C) 8 min.

D) 6 min.

135

MediumJEE Mains2021

Two spherical soap bubbles of radii r 1 and r 2 in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :

Options:

A) {{{r_1}{r_2}} \over {{r_1} + {r_2}}}

B) \sqrt {{r_1}{r_2}}

C) \sqrt {r_1^2 + r_2^2}

D) {{{r_1} + {r_2}} \over 2}

136

MediumJEE Mains2021

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y 1 and Y 2 . The combination behaves as a single wire then its Young's modulus is :

Options:

A) Y = {{2{Y_1}{Y_2}} \over {3({Y_1} + {Y_2})}}

B) Y = {{2{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}

C) Y = {{{Y_1}{Y_2}} \over {2({Y_1} + {Y_2})}}

D) Y = {{{Y_1}{Y_2}} \over {{Y_1} + {Y_2}}}

137

MediumJEE Mains2021

The length of a metal wire is l 1 , when the tension in it is T 1 and is l 2 when the tension is T 2 . The natural length of the wire is :

Options:

A) \sqrt {{l_1}{l_2}}

B) {{{l_1}{T_2} - {l_2}{T_1}} \over {{T_2} - {T_1}}}

C) {{{l_1}{T_2} + {l_2}{T_1}} \over {{T_2} + {T_1}}}

D) {{{l_1} + {l_2}} \over 2}

138

EasyJEE Mains2021

Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is :

Options:

A) {2^{{1 \over 3}}}:1

B) 1:{2^{{1 \over 3}}}

C) 2 : 1

D) 1 : 2

139

MediumJEE Mains2021

The value of tension in a long thin metal wire has been changed from T 1 to T 2 . The lengths of the metal wire at two different values of tension T 1 and T 2 are l 1 and l 2 respectively. The actual length of the metal wire is :

Options:

A) {{{l_1} + {l_2}} \over 2}

B) \sqrt {{T_1}{T_2}{l_1}{l_2}}

C) {{{T_1}{l_2} - {T_2}{l_1}} \over {{T_1} - {T_2}}}

D) {{{T_1}{l_1} - {T_2}{l_2}} \over {{T_1} - {T_2}}}

140

EasyJEE Mains2021

An object is located at 2 km beneath the surface of the water. If the fractional compression ${{\Delta V} \over V} is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given : density of water is 1000 kgm -3 and g = 9.8 ms -$2 ]

Options:

A) 1.44 $\times 10 7 Nm -$2

B) 1.44 $\times 10 9 Nm -$2

C) 1.96 $\times 10 7 Nm -$2

D) 2.26 $\times 10 9 Nm -$2

141

MediumJEE Mains2021

When two soap bubbles of radii a and b (b > a) coalesce, the radius of curvature of common surface is :

Options:

A) {{b - a} \over {ab}}

B) {{a + b} \over {ab}}

C) {{ab} \over {a + b}}

D) {{ab} \over {b - a}}

142

MediumJEE Mains2021

What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of water are 0.5 cm and 10 $-$3 Pa s, respectively. (Density of water : 10 3 kg/m 3 )

Options:

A) Steady flow to unsteady flow

B) Unsteady to steady flow

C) Remains turbulent flow

D) Remains steady flow

143

EasyJEE Mains2021

The pressure acting on a submarine is 3 $\times 10 5 Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be : (Assume that atmospheric pressure is 1 \times 10 5 Pa density of water is 10 3 kg m -3 , g = 10 ms -$2 )

Options:

A) {{200} \over 5}$%

B) {{200} \over 3}$%

C) {{3} \over 200}$%

D) {{5} \over 200}$%

144

MediumJEE Mains2021

The length of metallic wire is l 1 when tension in it is T 1 . It is l 2 when the tension is T 2 . The original length of the wire will be :

Options:

A) {{{T_1}{l_1} - {T_2}{l_2}} \over {{T_2} - {T_1}}}

B) {{{l_1} + {l_2}} \over 2}

C) {{{T_2}{l_1} + {T_1}{l_2}} \over {{T_1} + {T_2}}}

D) {{{T_2}{l_1} - {T_1}{l_2}} \over {{T_2} - {T_1}}}

145

MediumJEE Mains2021

A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be :

Options:

A) {{2T} \over J}\left( {{1 \over r} - {1 \over R}} \right)

B) {{3T} \over J}\left( {{1 \over r} - {1 \over R}} \right)

C) {{3T} \over rJ}

D) {{2T} \over rJ}

146

EasyJEE Mains2021

The normal density of a material is $\rho$ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :

Options:

A) {{\rho K} \over P}

B) {{PK} \over \rho }

C) {{\rho P} \over K}

D) {K \over {\rho P}}

147

MediumJEE Mains2021

If Y, K and $\eta $ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

Options:

A) Y = {{9K\eta } \over {3K - \eta }}N/{m^2}

B) Y = {{9K\eta } \over {2\eta + 3K}}N/{m^2}

C) \eta = {{3YK} \over {9K + Y}}N/{m^2}

D) K = {{Y\eta } \over {9\eta - 3Y}}N/{m^2}

148

MediumJEE Mains2020

A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms –1 at a point where the pressure is P pascal. At another point where pressure is ${P \over 2} Pascal its speed is V ms –1 . If the density of the fluid is \rho $ kg m –3 and the flow is streamline, then V is equal to :

Options:

A) \sqrt {{P \over {2\rho }} + {v^2}}

B) \sqrt {{P \over \rho } + {v^2}}

C) \sqrt {{{2P} \over \rho } + {v^2}}

D) \sqrt {{P \over \rho } + {v}}

149

MediumJEE Mains2020

An object of mass m is suspended at the end of a massless wire of length L and area of crosssection A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :

Options:

A) f = {1 \over {2\pi }}\sqrt {{{YA} \over {mL}}}

B) f = {1 \over {2\pi }}\sqrt {{{mL} \over {YA}}}

C) f = {1 \over {2\pi }}\sqrt {{{YL} \over {mA}}}

D) f = {1 \over {2\pi }}\sqrt {{{mA} \over {YL}}}

150

MediumJEE Mains2020

In an experiment to verify Stokes law, a small spherical ball of radius r and density $\rho $ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to : (ignore viscosity of air)

Options:

A) r

B) r 4

C) r 3

D) r 2

151

MediumJEE Mains2020

A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is ${{27} \over 8}$ w.r.t water, the value of r is :

Options:

A) {{2} \over 3}$R

B) {{4} \over 9}$R

C) {{1} \over 3}$R

D) {{8} \over 9}$R

152

MediumJEE Mains2020

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x 1 and in the other, x 2 . When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is:

Options:

A) gdS(x 2 + x 1 ) 2

B) gdS$\left( {x_2^2 + x_1^2} \right)

C) {1 \over 4}gdS{\left( {{x_2} - {x_1}} \right)^2}

D) {3 \over 4}gdS{\left( {{x_2} - {x_1}} \right)^2}

153

MediumJEE Mains2020

A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, B = 8 $ \times $ 10 10 Pa)

Options:

A) 0.6

B) 20

C) 1.67

D) 5

154

MediumJEE Mains2020

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s –2 . The density of water is 1 gm cm –3 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980 cm/s 2 ).

Options:

A) 1.52 gm

B) 4.51 gm

C) 3.15 gm

D) 4.15 gm

155

MediumJEE Mains2020

A metallic sphere cools from 50 o C to 40 o in 300 s. If atmospheric temperature around is 20 o C, then the sphere’s temperature after the next 5 minutes will be close to :

Options:

A) 35 o C

B) 31 o C

C) 33 o C

D) 28 o C

156

MediumJEE Mains2020

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :

Options:

A) 4 : 1

B) 8 : 1

C) 2 : 1

D) 0.8 : 1

157

MediumJEE Mains2020

A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0.05 Nm –1 , density = 667 kg m –3 ) which rises to height h in the tube. It is observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60 o with one another. Then h is close to (g = 10 ms –2 )

Options:

A) 0.049 m

B) 0.087 m

C) 0.137 m

D) 0.172 m

158

MediumJEE Mains2020

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is $\omega $ rad s –1 . The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be :

Options:

A) {{2{\omega ^2}} \over {25g}}

B) {{5{\omega ^2}} \over {2g}}

C) {{25{\omega ^2}} \over {2g}}

D) {{2{\omega ^2}} \over {5g}}

159

MediumJEE Mains2020

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:

Options:

A) 1 : 2

B) 2 : 1

C) 1:\sqrt 2

D) \sqrt 2 :1

160

MediumJEE Mains2020

A small spherical droplet of density d is floating exactly half immersed in a liquid of density $\rho $ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) :

Options:

A) r = \sqrt {{T \over {\left( {d - \rho } \right)g}}}

B) r = \sqrt {{{2T} \over {3\left( {d + \rho } \right)g}}}

C) r = \sqrt {{T \over {\left( {d + \rho } \right)g}}}

D) r = \sqrt {{{3T} \over {\left( {2d - \rho } \right)g}}}

161

MediumJEE Mains2020

Water flows in a horizontal tube (see figure). The pressure of water changes by 700 Nm –2 between A and B where the area of cross section are 40 cm 2 and 20 cm 2 , respectively. Find the rate of flow of water through the tube. (density of water = 1000 kgm –3 )

Options:

A) 1810 cm 3 /s

B) 2420 cm 3 /s

C) 3020 cm 3 /s

D) 2720 cm 3 /s

162

MediumJEE Mains2020

Two liquids of densities ${\rho _1} an {\rho _2} ({\rho _2} = 2{\rho _1}$) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing)

Options:

A) 1/3

B) 1/2

C) 1/4

D) 2/3

163

MediumJEE Mains2020

A leak proof cylinder of length 1m, made of a metal which has very low coefficient of expansion is floating vertically in water at 0°C such that its height above the water surface is 20 cm. When the temperature of water is increased to 4°C, the height of the cylinder above the water surface becomes 21 cm. The density of water at T = 4°C, relative to the density at T = 0°C is close to :

Options:

A) 1.04

B) 1.26

C) 1.01

D) 1.03

164

MediumJEE Mains2020

Consider a solid sphere of radius R and mass density $\rho \left( r \right) = {\rho _0}\left( {1 - {{{r^2}} \over {{R^2}}}} \right) , 0 < r \le R$ The minimum density of a liquid in which it will float is :

Options:

A) {{2{\rho _0}} \over 3}

B) {{2{\rho _0}} \over 5}

C) {{{\rho _0}} \over 5}

D) {{{\rho _0}} \over 3}

165

MediumJEE Mains2020

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :

Options:

A) {3 \over 4}

B) {9 \over {16}}

C) {{\sqrt 3 } \over 2}

D) {{81} \over {256}}

166

MediumJEE Mains2019

A solid sphere, of radius R acquires a terminal velocity v 1 when falling (due to gravity) through a viscous fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v 2 , when falling through the same fluid, the ratio (v 1 /v 2 ) equals :

Options:

A) {1 \over 9}

B) {1 \over {27}}

C) 27

D) 9

167

MediumJEE Mains2019

The number density of molecules of a gas depends on their distance r from the origin as, $n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}$. Then the total number of molecules is proportional to :

Options:

A) {n_0}{\alpha ^{ - 3/4}}

B) {n_0}{\alpha ^{ - 3}}

C) {n_0}{\alpha ^{1/4}}

D) \sqrt {{n_0}} {\alpha ^{1/2}}

168

MediumJEE Mains2019

A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to :

Options:

A) {{3F} \over {\left( {\pi {r^2}YT} \right)}}

B) {{6F} \over {\left( {\pi {r^2}YT} \right)}}

C) {F \over {\left( {3\pi {r^2}YT} \right)}}

D) {9F\left( {\pi {r^2}YT} \right)}

169

MediumJEE Mains2019

A submarine experiences a pressure of 5.05 × 10 6 Pa at a depth of d 1 in a sea. When it goes further to a depth of d 2 , it experiences a pressure of 8.08 × 10 6 Pa. Then d 2 –d 1 is approximately (density of water = 10 3 kg/m 3 and acceleration due to gravity = 10 ms –2 ) :

Options:

A) 600 m

B) 400 m

C) 300 m

D) 500 m

170

MediumJEE Mains2019

Water from a tap emerges vertically downwards with an initial speed of 1.0 ms –1 . The cross-sectional area of the tap is 10 –4 m 2 . Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, 0.15 m below the tap would be : (Take g = 10 ms –2 )

Options:

A) 5 × 10 –4 m 2

B) 2 × 10 –5 m 2

C) 5 × 10 –5 m 2

D) 1 × 10 –5 m 2

171

MediumJEE Mains2019

The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit?

Options:

A) 1.16 mm

B) 1.36 mm

C) 1.00 mm

D) 0.90 mm

172

MediumJEE Mains2019

A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take, density of water = 10 3 kg/m 3 ]

Options:

A) 30.1 kg

B) 87.5 kg

C) 65.4 kg

D) 46.3 kg

173

MediumJEE Mains2019

In an experiment, brass and steel wires of length 1 m each with areas of cross section 1mm 2 are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is, [Given, the Young's Modulus for steel and brass are, respectively, 120 × 10 9 N/m 2 and 60 × 10 9 N/m 2 ]

Options:

A) 8.0 × 10 6 N/m 2

B) 1.2 × 10 6 N/m 2

C) 0.2 × 10 6 N/m 2

D) 1.8 × 10 6 N/m 2

174

MediumJEE Mains2019

The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of thier densities is 13.6. Their contact angles, with glass, are close to 135° and 0°, respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius r 1 , while water rises by the same amount h in a capillary tube of radius r 2 . The ratio, (r 1 /r 2 ), is then close to :

Options:

A) 2/5

B) 2/3

C) 3/5

D) 4/5

175

MediumJEE Mains2019

A wooden block floating in a bucket of water has 4/5 of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is :-

Options:

A) 0.8

B) 0.7

C) 0.6

D) 0.5

176

MediumJEE Mains2019

A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 1/16 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is :

Options:

A) 2T\sqrt {{1 \over {10}}}

B) 4T\sqrt {{1 \over {14}}}

C) 4T\sqrt {{1 \over {15}}}

D) 2T\sqrt {{1 \over {14}}}

177

MediumJEE Mains2019

If 'M' is the mass of water that rises in a capillary tube of radius 'r', then mass of water which will rise in a capillary tube of radius '2r' is :

Options:

A) M

B) 4M

C) M/2

D) 2M

178

MediumJEE Mains2019

Young's moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to :-

Options:

A) 1.7 mm

B) 1.9 mm

C) 1.3 mm

D) 1.5 mm

179

MediumJEE Mains2019

Water from a pipe is coming at a rate of 100 litres per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water = 1000 kg/m 3 , coefficient of viscosity of water = 1mPas)

Options:

A) 10 6

B) 10 4

C) 10 3

D) 10 2

180

MediumJEE Mains2019

A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1 p ms –2 , what will be the tensile stress that would be developed in the wire ?

Options:

A) 3.1 × 10 6 Nm –2

B) 6.2 × 10 6 Nm –2

C) 4.8 × 10 6 Nm –2

D) 5.2 × 10 6 Nm –2

181

MediumJEE Mains2019

A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms –1 . Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to:

Options:

A) 10 4 Nm –2

B) 10 6 Nm –2

C) 10 8 Nm –2

D) 10 3 Nm –2

182

MediumJEE Mains2019

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational speed is 2 rotations per second, then the difference in the heights between the centre and the sides, in cm, will be :

Options:

A) 2.0

B) 1.2

C) 0.1

D) 0.4

183

MediumJEE Mains2019

A load of mass M kg is suspended from a steel wire of length 2m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is:

Options:

A) 5.0 mm

B) zero

C) 3.0 mm

Options:

A) \theta = {\tan ^{ - 1}}\pi \left( {{{{\rho _1}} \over {{\rho _2}}}} \right)

B) \theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1}} \over {{\rho _2}}}} \right)

C) \theta = {\tan ^{ - 1}}\left( {{{{\rho _1} - {\rho _2}} \over {{\rho _1} + {\rho _2}}}} \right)

D) \theta = {\tan ^{ - 1}}{\pi \over 2}\left( {{{{\rho _1} + {\rho _2}} \over {{\rho _1} - {\rho _2}}}} \right)

194

MediumInteger TypeJEE Mains

Answer: Enter a numeric value

195

MediumInteger TypeJEE Mains

Answer: Enter a numeric value

196

MediumJEE Mains2016

A bottle has an opening of radius a and length b. A cork of length b and radius (a + $\Delta a) where (\Delta a < < a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is \mu $ then the force needed to push the cork into the bottle is :

Options:

A) ($\pi \mu B b) \Delta $a

B) (2$\pi \mu B b) \Delta $a

C) ($\pi \mu $ B b) a

D) (4$\pi \mu B b) \Delta $a

197

MediumJEE Mains2016

A thin 1 m long rod has a radius of 5 mm. A force of 50 $\pi $kN is applied at one end to determine its Young’s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false ?

Options:

A) {{\Delta \gamma } \over \gamma }$ gets minimum contribution from the uncertainty in the length.

B) The figure of merit is the largest for the length of the rod.

C) The maximum value of $\gamma that can be determined is 2 \times $ 10 14 N/m 2

D) {{\Delta \gamma } \over \gamma }$ gets its maximum contribution from the uncertainty in strain

198

MediumJEE Mains2016

Consider a water jar of radius R that has water filled up to height H and is kept on astand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then :

Options:

A) x = r\left( {{H \over {H + h}}} \right)

B) x = r{\left( {{H \over {H + h}}} \right)^{{1 \over 2}}}

C) x = r{\left( {{H \over {H + h}}} \right)^{{1 \over 4}}}

D) x = r{\left( {{H \over {H + h}}} \right)^{{2}}}

199

MediumJEE Mains2016

A uniformly tapering conical wire is made from a material of Young’s modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3 R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal :

Options:

A) L $\left( {1 + {2 \over 9}{{Mg} \over {\pi Y{R^2}}}} \right)

B) L $\left( {1 + {1 \over 3}{{Mg} \over {\pi Y{R^2}}}} \right)

C) L $\left( {1 + {1 \over 9}{{Mg} \over {\pi Y{R^2}}}} \right)

D) L $\left( {1 + {2 \over 3}{{Mg} \over {\pi Y{R^2}}}} \right)

200

MediumJEE Mains2016

Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force F = − kv, where ‘k’ is a constant, on the body ? (Graphs are schematic and not drawn to scale)

Options:

201

MediumJEE Mains2014

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $R and making a circular contact of radius r with the bottom R and making a circular contact of radius r with the bottom of the vessel. If r < < R and the surface tension of water is T, value of r just before bubbles detach is: (density of water is {\rho _w}$)

Options:

A) {R^2}\sqrt {{{{\rho _w}g} \over {3T}}}

B) {R^2}\sqrt {{{{\rho _w}g} \over {6T}}}

C) {R^2}\sqrt {{{{\rho _w}g} \over {T}}}

D) {R^2}\sqrt {{{{2\rho _w}g} \over {3T}}}

202

MediumJEE Mains2014

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities ${d_1} and {d_2} are filled in the tube. Each liquid subtends {90^ \circ } angle at center. Radius joining their interface makes an angle \alpha with vertical. Radio {{{d_1}} \over {{d_2}}}$ is :

Options:

A) {{1 + \sin \,\alpha } \over {1 - \sin \,\alpha }}

B) {{1 + \cos \,\alpha } \over {1 - \cos \,\alpha }}

C) {{1 + \tan \,\alpha } \over {1 - \tan \,\alpha }}

D) {{1 + \sin \,\alpha } \over {1 - \cos \,\alpha }}

203

MediumJEE Mains2014

The pressure that has to be applied to the ends of a steel wire of length $10 cm to keep its length constant when its temperature is raised by {100^ \circ }C is: (For steel Young's modulus is 2 \times {10^{11}}\,\,N{m^{ - 2}} and coefficient of thermal expansion is 1.1 \times {10^{ - 5}}\,{K^{ - 1}}$ )

Options:

A) 2.2 \times {10^8}\,\,Pa

B) 2.2 \times {10^9}\,\,Pa

C) 2.2 \times {10^7}\,\,Pa

D) 2.2 \times {10^6}\,\,Pa

204

MediumJEE Mains2014

An open glass tube is immersed in mercury in such a way that a length of $8 cm extends above the mercury level. The open end of the tube is then closed and scaled and the tube is raised vertically up by additional 46 cm. What will be length of the air column above mercury in the tube now? (Atmospheric pressure =76 cm of Hg$)

Options:

A) 16 cm

B) 22 cm

C) 38 cm

D) 6 cm

205

MediumJEE Mains2013

If a piece of metal is heated to temperature $\theta and then allowed to cool in a room which is at temperature {\theta _0}, the graph between the temperature T of the metal and time t$ will be closest to

Options:

206

MediumJEE Mains2013

A uniform cylinder of length $L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density \sigma at equilibrium position. The extension {x_0}$ of the spring when it is in equilibrium is:

Options:

A) {{Mg} \over k}

B) {{Mg} \over k}\left( {1 - {{LA\sigma } \over M}} \right)

C) {{Mg} \over k}\left( {1 - {{LA\sigma } \over {2M}}} \right)

D) {{Mg} \over k}\left( {1 + {{LA\sigma } \over M}} \right)

207

MediumJEE Mains2012

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5 \times {10^{ - 2}}\,\,N (see figure). The length of the slider is 30 cm$ and its weight negligible. The surface tension of the liquid film is

Options:

A) 0.0125\,\,N{m^{ - 1}}

B) 0.1\,\,N{m^{ - 1}}

C) 0.05\,\,N{m^{ - 1}}

D) 0.025\,\,N{m^{ - 1}}

208

MediumJEE Mains2012

A liquid in a beaker has temperature $\theta \left( t \right) at time t and {\theta _0} is temperature of surroundings, then according to Newton's law of cooling the correct graph between {\log _e}\left( {\theta - {\theta _0}} \right) and t$ is :

Options:

209

MediumJEE Mains2011

Work done in increasing the size of a soap bubble from a radius of $3 cm to 5 cm is nearly (Surface tension of soap solution = 0.03N{m^{ - 1}},

Options:

A) 0.2\pi mJ

B) 2\pi mJ

C) 0.4\pi mJ

D) 4\pi mJ

210

MediumJEE Mains2011

Water is flowing continuously from a tap having an internal diameter $8 \times {10^{ - 3}}\,\,m. The water velocity as it leaves the tap is 0.4\,\,m{s^{ - 1}} . The diameter of the water stream at a distance 2 \times {10^{ - 1}}\,\,m$ below the tap is close to :

Options:

A) 7.5 \times {10^{ - 3}}m

B) 9.6 \times {10^{ - 3}}m

C) 3.6 \times {10^{ - 3}}m

D) 5.0 \times {10^{ - 3}}m

211

MediumJEE Mains2010

A ball is made of a material of density $\rho where {\rho _{oil}}\, < \rho < {\rho _{water}} with {\rho _{oil}} and {\rho _{water}}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?

Options:

212

MediumJEE Mains2009

Two wires are made of the same material and have the same volume. However wire $1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of wire 1 increases by \Delta x on applying force F, how much force is needed to stretch wire 2$ by the same amount?

Options:

A) 4F

B) 6F

C) 9F

D) F

213

MediumJEE Mains2008

A spherical solid ball of volume $V is made of a material of density {\rho _1}. It is falling through a liquid of density {\rho _2}\left( {{\rho _2} < {\rho _1}} \right). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., {F_{viscous}} = - k{v^2}\left( {k > 0} \right).$ The terminal speed of the ball is

Options:

A) \sqrt {{{Vg\left( {{\rho _1} - {\rho _2}} \right)} \over k}}

B) {{{Vg{\rho _1}} \over k}}

C) \sqrt {{{Vg{\rho _1}} \over k}}

D) {{Vg\left( {{\rho _1} - {\rho _2}} \right)} \over k}

214

MediumJEE Mains2008

A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

Options:

215

MediumJEE Mains2008

A jar is filled with two non-mixing liquids $1 and 2 having densities {\rho _1} and {\rho _2} respectively. A solid ball, made of a material of density {\rho _3}, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for {\rho _1} , {\rho _1} and {\rho _3}$ ?

Options:

A) {\rho _3} < {\rho _1} < \rho {}_2

B) {\rho _1} > {\rho _3} > \rho {}_2

C) {\rho _1} < {\rho _2} < \rho {}_3

D) {\rho _1} < {\rho _3} < \rho {}_2

216

MediumJEE Mains2006

If the terminal speed of a sphere of gold (density $ = 19.5\,\,kg/{m^3}) is 0.2 m/s in a viscous liquid (density = 1.5\,\,kg/{m^3}, find the terminal speed of a sphere of silver (density = 10.5\,\,kg/{m^3}$) of the same size in the same liquid

Options:

A) 0.4 m/s

B) 0.133 m/s

C) 0.1 m/s

D) 0.2 m/s

217

MediumJEE Mains2006

A wire elongates by $l mm when a LOAD W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm$)

Options:

A) l

B) 2l

C) zero

D) l/2

218

MediumJEE Mains2005

A $20 cm long capillary tube is dipped in water. The water rises up to 8 cm.$ If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

Options:

A) 10 cm

B) 8 cm

C) 20 cm

D) 4 cm

219

MediumJEE Mains2005

If $S is stress and Y$ is young's modulus of material of a wire, the energy stored in the wire per unit volume is

Options:

A) {{{S^2}} \over {2Y}}

B) 2{S^2}Y

C) {S \over {2Y}}

D) {{2Y} \over {{S^2}}}

220

MediumJEE Mains2004

Spherical balls of radius $R are falling in a viscous fluid of viscosity \eta with a velocity v.$ The retarding viscous force acting on the spherical ball is

Options:

A) inversely proportional to both radius $R and velocity v

B) directly proportional to both radius $R and velocity v

C) directly proportional to $R but inversely proportional to v

D) inversely proportional to $R, but directly proportional to velocity v

221

MediumJEE Mains2004

A wire fixed at the upper end stretches by length $l by applying a force F.$ The work done in stretching is

Options:

A) 2Fl

B) Fl

C) {F \over {2l}}

D) {{Fl} \over 2}

222

MediumJEE Mains2004

If two soap bubbles of different radii are connected by a tube

Options:

A) air flows from the smaller bubble to the bigger

B) air flows from bigger bubble to the smaller bubble till the sizes are interchanged

C) air flows from the bigger bubble to the smaller bubble till the sizes become equal

D) there is no flow of air.

223

MediumJEE Mains2003

According to Newton's law of cooling, the rate of cooling of a body is proportional to ${\left( {\Delta \theta } \right)^n}, where {\Delta \theta } is the difference of the temperature of the body and the surrounding, and n$ is equal to :

Options:

A) two

B) three

C) four

Options:

A) \frac{d^2 y}{d x^2}=\sqrt{\frac{\rho g}{s}}

B) \frac{d y}{d x}=\sqrt{\frac{\rho g}{s}} x

C) \frac{d^2 y}{d x^2}=\frac{\rho g}{s} x

D) \frac{d^2 y}{d x^2}=\frac{\rho g}{s} y

322

MediumNEET2024

An ideal fluid is flowing in a non-uniform cross-sectional tube $X Y (as shown in the figure) from end X to end Y. If K_1 and K_2 are the kinetic energy per unit volume of the fluid at X and Y$ respectively, then the correct option is :

Options:

A) K_1=K_2

B) 2 K_1=K_2

C) K_1>K_2

D) K_1 < K_2

323

MediumNEET2024

The maximum elongation of a steel wire of $1 \mathrm{~m} length if the elastic limit of steel and its Young's modulus, respectively, are 8 \times 10^8 \mathrm{~N} \mathrm{~m}^{-2} and 2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$, is:

Options:

A) 4 mm

B) 0.4 mm

C) 40 mm

D) 8 mm

324

MediumNEET2024

A thin flat circular disc of radius $4.5 \mathrm{~cm} is placed gently over the surface of water. If surface tension of water is 0.07 \mathrm{~N} \mathrm{~m}^{-1}$, then the excess force required to take it away from the surface is

Options:

A) 19.8 mN

B) 198 N

C) 1.98 mN

D) 99 N

325

MediumNEET2024

A metallic bar of Young's modulus, $0.5 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2} and coefficient of linear thermal expansion 10^{-5}{ }^{\circ} \mathrm{C}^{-1}, length 1 \mathrm{~m} and area of cross-section 10^{-3} \mathrm{~m}^2 is heated from 0^{\circ} \mathrm{C} to 100^{\circ} \mathrm{C}$ without expansion or bending. The compressive force developed in it is :

Options:

A) 5 \times 10^3 \mathrm{~N}

B) 50 \times 10^3 \mathrm{~N}

C) 100 \times 10^3 \mathrm{~N}

D) 2 \times 10^3 \mathrm{~N}

326

MediumNEET2023

The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length $100 \mathrm{~cm} to stretch it by 1 \mathrm{~mm} is (if Young's modulus of the wire =2.0 \times 10^{11} \mathrm{Nm}^{-2}$ ) :

Options:

A) 10^{11}

B) 10^{17}

C) 10^7

D) 10^5

327

MediumNEET2023

Which of the following statement is not true?

Options:

A) Coefficient of viscosity is a scalar quantity

B) Surface tension is a scalar quantity

C) Pressure is a vector quantity

D) Relative density is a scalar quantity

328

MediumNEET2023

The viscous drag acting on a metal sphere of diameter $1 \mathrm{~mm}, falling through a fluid of viscosity 0.8 \mathrm{~Pa} s with a velocity of 2 \mathrm{~m} \mathrm{~s}^{-1}$ is equal to :

Options:

A) 15 \times 10^{-3} \mathrm{~N}

B) 30 \times 10^{-3} \mathrm{~N}

C) 1.5 \times 10^{-3} \mathrm{~N}

D) 20 \times 10^{-3} \mathrm{~N}

329

MediumNEET2023

The amount of energy required to form a soap bubble of radius $2 \mathrm{~cm} from a soap solution is nearly: (surface tension of soap solution =0.03 \mathrm{~N} \mathrm{~m}^{-1}$ )

Options:

A) 5.06 \times 10^{-4} \mathrm{~J}

B) 3.01 \times 10^{-4} \mathrm{~J}

C) 50.1 \times 10^{-4} \mathrm{~J}

D) 30.16 \times 10^{-4} \mathrm{~J}

330

MediumNEET2023

The venturi-meter works on :

Options:

A) Bernoulli's principle

B) The principle of parallel axes

C) The principle of perpendicular axes

D) Huygen's principle

331

MediumNEET2023

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W attached at its free end. The longitudinal stress at any point of cross-sectional area A$ of the wire is :

Options:

A) W / A

B) W / 2 A

C) Zero

D) 2 W / A

332

MediumNEET2022

Two copper vessels A and B have the same base area but of different shapes. A takes twice the volume of water as that B requires to fill upto a particular common height. Then the correct statement among the following is :

Options:

A) Vessel B weighs twice that of A.

B) Pressure on the base area of vessels A and B is same.

C) Pressure on the base area of vessels A and B is not same.

D) Both vessels A and B weigh the same.

333

MediumNEET2022

The terminal velocity of a copper ball of radius 5 mm falling through a tank of oil at room temperature is 10 cm s $-1 . If the viscosity of oil at room temperature is 0.9 kg m -1 s -$1 , the viscous drag force is :

Options:

A) 4.23 $\times 10 -$6 N

B) 8.48 $\times 10 -$3 N

C) 8.48 $\times 10 -$5 N

D) 4.23 $\times 10 -$3 N

334

MediumNEET2022

A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball (v) as a function of time (t) is

Options:

A) A

B) B

C) C

D) D

335

MediumNEET2022

If a soap bubble expands, the pressure inside the bubble

Options:

A) Decreases

B) Increases

C) Remains the same

D) Is equal to the atmospheric pressure

336

MediumNEET2022

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The stretching of a spring is determined by the shear modulus of the material of the spring. Reason (R) : A coil spring of copper has more tensile strength than a steel spring of same dimensions. In the light of the above statements, choose the most appropriate answer from the options given below:

Options:

A) Both (A) and (R) are true and (R) is the correct explanation of (A)

B) Both (A) and (R) are true and (R) is not the correct explanation of (A)

C) (A) is true but (R) is false

D) (A) is false but (R) is true

337

MediumNEET2021

The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerin becomes constant after some time. If the density of glycerin is ${d \over 2}$, then the viscous force acting on the ball will be :

Options:

A) 2Mg

B) {{Mg} \over 2}

C) Mg

D) {{3} \over 2}$Mg

338

MediumNEET2020

A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in Water. The mass of water that will rise in this tube is :

Options:

A) 5.0 g

B) 10.0 g

C) 20.0 g

D) 2.5 g

339

MediumNEET2020

A wire of length L, are of cross section A is hanging from a fixed support. The length of the wire changed to L 1 when mass M is suspended from its free end. The expression for Young's modulus is :

Options:

A) {{Mg\left( {{L_1} - L} \right)} \over {AL}}

B) {{MgL} \over {A{L_1}}}

C) {{MgL} \over {A\left( {{L_1} - L} \right)}}

D) {{Mg{L_1}} \over {AL}}

340

MediumNEET2019

The unit of thermal conductivity is :

Options:

A) J m –1 K –1

B) W m K –1

C) J m K –1

D) W m –1 K –1

341

MediumNEET2019

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + $l$). The elastic potential energy stored in the extended wire is :

Options:

A) Mgl

B) mgL

C) {1 \over 2}$Mgl

D) {1 \over 2}$MgL

342

MediumNEET2019

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 $ \times $ 10 –2 N/m. The pressure inside the bubble equals at a point Z 0 below the free surface of water in a container. Taking g = 10 m/s 2 , density of water = 10 3 kg/m 3 , the value of Z 0 is :

Options:

A) 1 cm

B) 10 cm

C) 100 cm

D) 0.5 cm

343

MediumNEET2019

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in tmperature. The length of aluminium rod is : ($\alpha Cu = 1.7 × 10 –5 K –1 and \alpha $ Al = 2.2 × 10 –5 K –1 )

Options:

A) 119.9 cm

B) 88 cm

C) 68 cm

D) 6.8 cm

344

MediumNEET2019

A small hole of area of cross-section 2 mm 2 present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s 2 , the rate of flow of water through the open hole would be nearly :

Options:

A) 8.9 × 10 –6 m 3 /s

B) 2.23 × 10 –6 m 3 /s

C) 6.4 × 10 –6 m 3 /s

D) 12.6 × 10 –6 m 3 /s

345

MediumNEET2018

A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

Options:

A) r 3

B) r 2

C) r 5

D) r 4

346

MediumNEET2018

The power radiated by a black body is P and it radiates maximum energy at wavelength, $\lambda 0 . If the temperature of the black body is now changed so that it radiates maximum energy at wavelength {3 \over 4}{\lambda _0}$, the power radiated by it becomes nP. The value of n is

Options:

A) {3 \over 4}

B) {4 \over 3}

C) {{256} \over {81}}

D) {{81} \over {256}}

347

MediumNEET2018

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by $\Delta $l on applying a force F, how much force is needed to stretch the second wire by the same amount?

Options:

A) 6F

B) F

C) 9F

D) 4F

348

MediumNEET2017

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K 1 and K 2 . The thermal conductivity of the composite will be

Options:

A) {{3\left( {{K_1} + {K_2}} \right)} \over 2}

B) {K_1} + {K_2}

C) 2\left( {{K_1} + {K_2}} \right)

D) {{{K_1} + {K_2}} \over 2}

349

MediumNEET2017

The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'P', the fractional decrease in radius is

Options:

A) {B \over {3p}}

B) {{3p} \over B}

C) {p \over {3B}}

D) {p \over B}

350

MediumNEET2017

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is

Options:

A) 425 kg m $-$3

B) 800 kg m $-$3

C) 928 kg m $-$3

D) 650 kg m $-$3

351

MediumNEET2017

A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be

Options:

A) 450

B) 1000

C) 1800

D) 225

352

MediumNEET2016

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at 100 o C, while the other one is at 0 o C. If the two bodies are brought into contact, then, assuming no heat loss, the final common temperature is

Options:

A) 50 o C

B) more than 50 o C

C) less than 50 o C but greater than 0 o C

D) 0 o C

353

MediumNEET2016

Three liquids of densities $\rho 1 , \rho 2 and \rho 3 (with \rho 1 > \rho 2 > \rho 3 ), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact \theta 1 , \theta 2 and \theta $ 3 obey

Options:

A) {\pi \over 2} > {\theta _1} > {\theta _2} > {\theta _3} \ge 0

B) 0 $ \le \theta 1 < \theta 2 < \theta 3 < {\pi \over 2}

C) {\pi \over 2} < {\theta _1} < {\theta _2} < {\theta _3} < \pi

D) \pi > {\theta _1} > {\theta _2} > {\theta _3} > {\pi \over 2}

354

MediumNEET2016

A rectangular film of liquid is extended from (4 cm $ \times 2 cm) to (5 cm \times 4 cm). If the work done is 3 \times 10 -$4 J, the value of the surface tension of the liquid is

Options:

A) 0.250 N m $-$1

B) 0.125 N m $-$1

C) 0.2 N m $-$1

D) 8.0 N m $-$1

355

MediumNEET2016

A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

Options:

A) {7 \over 4}\,$ T

B) {3 \over 2}$ T

C) {4 \over 3}$ T

D) T

356

MediumNEET2016

Two non-mixing liquids of densities $\rho and n\rho (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length \rho L (\rho $ < 1) in the denser liquid. The density d is equal to

Options:

A) \left\{ {2 + \left( {n - 1} \right)p} \right\}\rho

B) \left\{ {1 + \left( {n - 1} \right)p} \right\}\rho

C) \left\{ {1 + \left( {n + 1} \right)p} \right\}\rho

D) \left\{ {2 + \left( {n + 1} \right)p} \right\}\rho

357

MediumNEET2016

A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U 1 , at wavelength 500 nm is U 2 and that at 1000 nm is U 3 . Wien's constant, b = 2.88 $ \times $ 10 6 nm K. Which of the following is correct ?

Options:

A) U 1 > U 2

B) U 2 > U 1

C) U 1 = 0

D) U 3 = 0

358

MediumNEET2016

Coefficient of linear expansion of brass and steel rods are $\alpha 1 and \alpha 2 . Lengths of brass and steel rods are l 1 and l 2 respectively. If (l 1 - l$ 2 ) is maintained same at all temperatures, which one of the following relations holds good?

Options:

A) \alpha 1 l 2 = \alpha 2 2 l$ 1

B) \alpha 1 l 1 = \alpha $ 2 l 2

C) \alpha 1 l 2 = \alpha 2 l$ 1

D) \alpha 1 l 2 2 = \alpha 2 l$ 1 2

359

MediumNEET2016

A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h [Latent heat of ice is $3.4 \times {10^5}$ J/kg and g = 10 N/Kg]

Options:

A) 136 km

B) 68 km

C) 34 km

D) 544 km

360

MediumNEET2015

Water rises to a height h in capillary tube. If the length of capillary tube above the surface of water is made less than h, then

Options:

A) water rises upto a point a little below the top and stays there.

B) water does not rise at all.

C) water rises upto the tip of capillary tube and then starts overflowing like a fountain.

D) water rises upto the top of capillary tube and stays there without overflowing.

361

MediumNEET2015

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of

Options:

A) 4 : 1

B) 1 : 1

C) 1 : 2

D) 2 : 1

362

MediumNEET2015

The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the holes is

Options:

A) {{VR{}^2} \over {{n^3}{r^2}}}

B) {{{V^2}R} \over {nr}}

C) {{V{R^2}} \over {{n^2}{r^2}}}

D) {{V{R^2}} \over {n{r^2}}}

363

MediumNEET2015

The value of coefficient of volume expansion of glycerin is 5 $ \times 10 -4 K -$1 . The fractional change in the density of glycerin for a rise of 40 o C in its temperature, is

Options:

A) 0.025

B) 0.010

C) 0.015

D) 0.020

364

MediumNEET2015

The two ends of a metal rod are maintained at temperatures 100 o C and 110 o C. The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures 200 o C and 210 o C, the rate of heat flow will be

Options:

A) 8.0 J/s

B) 4.0 J/s

C) 44.0 J/s

D) 16.8 J/s

365

MediumNEET2015

The approximate depth of an ocean is 2700 m. The compressiblity of water is 45.4 $ \times 10 -11 Pa -$1 and density of water is 10 3 kg/m 3 . What fractional compression of water will be obtained at the bottom of the ocean?

Options:

A) 1.2 $ \times 10 -$2

B) 1.4 $ \times 10 -$2

C) 0.8 $ \times 10 -$2

D) 1.0 $ \times 10 -$2

366

MediumNEET2015

On observing light from three different starts P, Q and R, it was found that intensity of violet colour is maximum in the spectrum of P, the intensity of green colour is maximum in the spectrum of R and the intensity of red colour is maximum in the spectrum of Q. If T P , T Q and T R are the respective absolute temperatures of P, Q and R, then it can be conclued from the above observations that

Options:

A) T P < T R < T Q

B) T P < T Q < T R

C) T P > T Q > T R

D) T P > T R > T Q

367

MediumNEET2015

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m 2 . Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $({\rho _{air}} = 1.2kg/{m^3})

Options:

A) 2.4 $ \times $ 10 5 N, upwards

B) 2.4 $ \times $ 10 5 N, downwards

C) 4.8 $ \times $ 10 5 N, downwards

D) 4.8 $ \times $ 10 5 N, upwards

368

MediumNEET2014

A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

Options:

A) energy = 4VT $\left( {{1 \over r} - {1 \over R}} \right)$ is released.

B) energy = 3VT$\left( {{1 \over r} + {1 \over R}} \right)$ is absorbed.

C) energy = 3VT$\left( {{1 \over r} - {1 \over R}} \right)$ is released

D) energy is neither released nor absorbed.

369

MediumNEET2014

Certain quantity of water cools from 70 o C to 60 o C in the first 5 minutes and to 54 o C in the next 5 minutes. The temperature of the surroundings is

Options:

A) 45 o C

B) 20 o C

C) 42 o C

D) 10 o C

370

MediumNEET2014

Steam at 100 o C is passed into 20 g of water at 10 o C. When water acquires a temperature of 80 o C, the mass of water present will be [Take specific heat of water = 1 cal g $-1 o C -1 and latent heat of steam = 540 cal g -$1 ]

Options:

A) 24 g

B) 31.5 g

C) 42.5 g

D) 22.5 g

371

MediumNEET2014

Copper of fixed volume V is drawn into wire of length $l. When this wire is subjected to a constant force F, the extension produced in the wire is \Delta l$. Which of the following graphs is a straight line ?

Options:

A) \Delta l versus 1/l

B) \Delta l versus l$ 2

C) \Delta l versus 1/l$ 2

D) \Delta l versus l

372

MediumNEET2013

The density of water at 20 o C is 998 kg/m 3 and at 40 o C is 992 kg/m 3 . The coefficient of volume expansion of water is

Options:

A) 3 $ \times 10 -$4 / o C

B) 2 $ \times 10 -$4 / o C

C) 6 $ \times 10 -$4 / o C

D) 10 $ \times 10 -$4 / o C

373

MediumNEET2013

Two metal rods 1 and 2 of same lengths have same temperature difference between their ends. Their thermal conductivities are K 1 and K 2 and cross sectional areas A 1 and A 2 , respectively. If the rate of heat conduction in 1 is four times that in 2, then

Options:

A) K 1 A 1 = 4K 2 A 2

B) K 1 A 1 = 2K 2 A 2

C) 4K 1 A 1 = K 2 A 2

D) K 1 A 1 = K 2 A 2

374

MediumNEET2013

If the ratio of diameters, lengths and Young's modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be

Options:

A) \left( {{{5q} \over {7s{p^2}}}} \right)

B) \left( {{{7q} \over {5s{p^2}}}} \right)

C) \left( {{{2q} \over {5sp}}} \right)

D) \left( {{{7q} \over {5sp}}} \right)

375

MediumNEET2013

A fluid is in streamline flow across a horizontal pipe of variable area of cross section. For this which of the following statements is correct?

Options:

A) The velocity is maximum at the narrowest part of the pipe and pressure is maximum at the widest part of the pipe.

B) Velocity and pressure both are maximum at the narrowest part of the pipe.

C) velocity and pressure both are maximum at the widest part of the pipe.

D) The velocity is minimum at the narrowest part of the pipe and the pressure is minimum at the widest part of the pipe.

376

MediumNEET2013

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

Options:

A) length = 200 cm, diameter = 2 mm

B) length = 300 cm, diameter = 3 mm

C) length = 50 cm, diameter = 0.5 mm

D) length = 100 cm, diameter = 1 mm

377

MediumNEET2013

The wettability of a surface by a liquid depends primarily on

Options:

A) density

B) angle of contact between the surface and the liquid

C) viscosity

D) surface tension

378

MediumNEET2013

A piece of iron is heated in a flame. It first becomes dull red then becomes reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using

Options:

A) Kirchhoff's Law

B) Newton's Law of cooling

C) Stefan's Law

D) Wien's displacement Law

379

MediumNEET2013

The molar specific heats of an ideal gas at constant pressure and volume are denoted by C p and C v , respectively. If $\gamma = {{{C_p}} \over {{C_v}}}$ and R is the universal gas constant, then C v is equal to

Options:

A) {{\left( {\gamma - 1} \right)} \over R}

B) \gamma R

C) {{1 + \gamma } \over {1 - \gamma }}

D) {R \over {\left( {\gamma - 1} \right)}}

380

MediumNEET2012

A slab of stone of area 0.36 m 2 and thickness 0.1 m is exposed on the lower surface to steam at 100 o C. A block of ice at 0 o C rests on the upper surface of the slab. In one hour 4.8 kg of ice is melted. The thermal conductivity of slab is (Given latent heat of fusion of ice = 3.36 $ \times 10 5 J kg -$1 )

Options:

A) 1.24 J/m/s/ o C

B) 1.29 J/m/s/ o C

C) 2.05 J/m/s/ o C

D) 1.02 J/m/s/ o C

381

MediumNEET2012

If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q?

Options:

A) {Q \over {4\pi {R^2}\sigma }}

B) {\left( {{Q \over {4\pi {R^2}\sigma }}} \right)^{ - 1/2}}

C) {\left( {{{4\pi {R^2}Q} \over \sigma }} \right)^{1/4}}

D) {\left( {{Q \over {4\pi {R^2}\sigma }}} \right)^{1/4}}

382

MediumNEET2012

Liquid oxygen at 50 K is heated to 300 K at constant pressure of 1 atm. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time ?

Options:

383

MediumNEET2010

A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod, when placed in thermal contact with the two reservoirs in time t?

Options:

A) {Q \over 4}

B) {Q \over {16}}

C) 2Q

D) {Q \over 2}

384

MediumNEET2010

The total radiant energy per unit area, normal to the direction of incidence, received at a distance R from the centre of a star of radius r, whose outer surface radiates as a black body at a temperature TK is given by

Options:

A) {{\sigma {r^2}{T^4}} \over {{R^2}}}

B) {{\sigma {r^2}{T^4}} \over {4\pi {R^2}}}

C) {{\sigma {r^2}{T^4}} \over {{R^4}}}

D) {{4\pi \sigma {r^2}{T^4}} \over {{R^2}}}

385

MediumNEET2010

Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t o C, the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is where $\sigma $ is the Stefan's constant.

Options:

A) {{{r^2}\sigma {{\left( {t + 273} \right)}^4}} \over {4\pi {R^2}}}

B) {{16{\pi ^2}{r^2}\sigma {t^4}} \over {{R^2}}}

C) {{{r^2}\sigma {{\left( {t + 273} \right)}^4}} \over {{R^2}}}

D) {{4\pi {r^2}\sigma {t^4}} \over {{R^2}}}

386

MediumNEET2009

The two ends of a rod of length L and a uniform cross-sectional area A are Kept at two temperatures T 1 and T 2 (T 1 > T 2 ). The rate of heat transfer, ${{dQ} \over {dt}}$ through the rod in a steady state is given by :

Options:

A) {{dQ} \over {dt}} = {{k\left( {{T_1} - {T_2}} \right)} \over {LA}}

B) {{dQ} \over {dt}} = kLA({T_1} - {T_2})

C) {{dQ} \over {dt}} = {{kA\left( {{T_1} - {T_2}} \right)} \over L}

D) {{dQ} \over {dt}} = {{kL\left( {{T_1} - {T_2}} \right)} \over A}

387

MediumNEET2009

A black body at 227 o C radiates heat at the rate of 7 cals/cm 2 s. At a temperature of 727 o C, the rate of heat radiated in the same units will be

Options:

A) 50

B) 112

C) 80

D) 60

388

MediumNEET2008

On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are 39 o W and 239 o W respectively. What will be the temperature on the new scale, corresponding to a temperature of 39 o C on the Celsius scale ?

Options:

A) 200 o W

B) 139 o W

C) 78 o W

D) 117 o W

389

MediumNEET2007

Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t o C, the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is where $\sigma $ is the Stefan's constant.

Options:

A) {{{r^2}\sigma {{\left( {t + 273} \right)}^4}} \over {4\pi {R^2}}}

B) {{16{\pi ^2}{r^2}\sigma {t^4}} \over {{R^2}}}

C) {{{r^2}\sigma {{\left( {t + 273} \right)}^4}} \over {{R^2}}}

D) {{4\pi {r^2}\sigma {t^4}} \over {{R^2}}}

390

MediumNEET2007

A black body is at 727 o C. It emits energy at a rate which is proportional to

Options:

A) (1000) 4

B) (1000) 2

C) (727) 4

D) (727) 2

391

MediumNEET2006

A black body at 1227 o C emits radiations with maximum intensity at a wavelength of 5000 $\mathop A\limits^ \circ $. If the temperature of the body is increased by 1000 o C, the maximum intensity will be observed at

Options:

A) 3000 $\mathop A\limits^ \circ

B) 4000$\mathop A\limits^ \circ

C) 5000$\mathop A\limits^ \circ

D) 6000$\mathop A\limits^ \circ

392

MediumNEET2005

Which of the following rods, (given radius r and length $l$) each made of the same material and whose ends are maintained at the same temperature will conduct most heat ?

Options:

A) r = r 0 , $l = l$ 0

B) r = 2r 0 , $l = l$ 0

C) r = r 0 , $l = 2l$ 0

D) r = 2r 0 , $l = 2l$ 0

393

MediumNEET2004

If $\lambda $ m denotes the wavelength at which the radioactive amission from a black body at a temperature TK is maximum, then

Options:

A) {\lambda _m}\, \propto \,{T^4}

B) {\lambda _m}$ is independent of T

C) {\lambda _m} \propto $ T

D) {\lambda _m}\, \propto \,{T^{ - 1}}

394

MediumNEET2003

Consider a compound slab consisting of two different materials having equal thicknesses and thermal conductivities K and 2K, respectively. The equivalent thermal conductivity of the slab is

Options:

A) {2 \over 3}K

B) \sqrt 2 K

C) 3 K

D) {4 \over 3}K

395

MediumNEET2002

Unit of Stefan's constant is

Options:

A) watt m 2 K 4

B) watt m 2 /K 4

C) watt/m 2 K

D) watt/m 2 K 4

396

MediumNEET2002

Which of the following is best close to an ideal black body?

Options:

A) black lamp

B) cavity maintained at constant temperature

C) platinium black

D) a lump of charcoal heated to high temperature.

397

MediumNEET2002

Consider two rods of same length and different specific heats (S 1 , S 2 ), conductivities (K 1 , K 2 ) and area of cross-sections (A 1 , A 2 ) and both having temperatures T 1 and T 2 at their ends. If rate of loss of heat due to conduction is equal, then

Options:

A) K 1 A 1 = K 2 A 2

B) {{{K_1}{A_1}} \over {{S_1}}} = {{{K_2}{A_2}} \over {{S_2}}}

C) K 2 A 1 = K 1 A 2

D) {{{K_2}{A_1}} \over {{S_2}}} = {{{K_1}{A_2}} \over {{S_1}}}

398

MediumNEET2002

For a black body at temperature 727 o C, its radiating power is 60 watt and temperature of surrounding is 227 o C. If temperature of black body is changed to 1227 o C then its radiating power will be

Options:

A) 304 W

B) 320 W

C) 240 W

D) 120 W

399

MediumNEET2002

The Wien's displacement law express relation between

Options:

A) wavelength corresponding to maximum energy and temperature

B) radiation energy and wavelength

C) temperature and wavelength

D) colour of light and temperature.

400

MediumNEET2001

A cylindrical rod having temperature T 1 and T 2 at its end. The rate of flow of heat Q 1 cal/sec. If all the linear dimension are doubled keeping temperature constant, then rate of flow of heat Q 2 will be

Options:

A) 4Q 1

B) 2Q 1

C) {{{Q_1}} \over 4}

D) {{{Q_1}} \over 2}

401

MediumNEET2000

A black body has maximum wavelength $\lambda $ m at 2000 K. Its corresponding wavelength at 3000 K will be

Options:

A) {3 \over 2}{\lambda _m}

B) {2 \over 3}{\lambda _m}

C) {{16} \over {81}}{\lambda _m}

D) {{81} \over {16}}{\lambda _m}

402

MediumJEE Advanced2024

A table tennis ball has radius (3 / 2) \times 10^{-2} \mathrm{~m} and mass (22 / 7) \times 10^{-3} \mathrm{~kg}. It is slowly pushed down into a swimming pool to a depth of d=0.7 \mathrm{~m} below the water surface and then released from rest. It emerges from the water surface at speed v, without getting wet, and rises up to a height H. Which of the following option(s) is(are) correct? [Given: \pi=22 / 7, g=10 \mathrm{~m} \mathrm{~s}^{-2}, density of water =1 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}, viscosity of water =1 \times 10^{-3} \mathrm{~Pa}-s.]

Options:

A) The work done in pushing the ball to the depth d is 0.077 \mathrm{~J}.

B) If we neglect the viscous force in water, then the speed v=7 \mathrm{~m} / \mathrm{s}.

C) If we neglect the viscous force in water, then the height H=1.4 \mathrm{~m}.

D) The ratio of the magnitudes of the net force excluding the viscous force to the maximum viscous force in water is 500 / 9.

403

HardJEE Advanced2022

A bubble has surface tension S. The ideal gas inside the bubble has ratio of specific heats \gamma= \frac{5}{3}. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is P_{a 1}, the radius of the bubble is found to be r_{1} and the temperature of the enclosed gas is T_{1}. When the atmospheric pressure is P_{a 2}, the radius of the bubble and the temperature of the enclosed gas are r_{2} and T_{2}, respectively. Which of the following statement(s) is(are) correct?

Options:

A) If the surface of the bubble is a perfect heat insulator, then \left(\frac{r_{1}}{r_{2}}\right)^{5}=\frac{P_{a 2}+\frac{2 S}{r_{2}}}{P_{a 1}+\frac{2 S}{r_{1}}}.

B) If the surface of the bubble is a perfect heat insulator, then the total internal energy of the bubble including its surface energy does not change with the external atmospheric pressure.

C) If the surface of the bubble is a perfect heat conductor and the change in atmospheric temperature is negligible, then \left(\frac{r_{1}}{r_{2}}\right)^{3}=\frac{P_{a 2}+\frac{4 S}{r_{2}}}{P_{a 1}+\frac{4 S}{r_{1}}}.

D) If the surface of the bubble is a perfect heat insulator, then \left(\frac{T_{2}}{T_{1}}\right)^{\frac{5}{2}}=\frac{P_{a 2}+\frac{4 S}{r_{2}}}{P_{a 1}+\frac{4 S}{r_{1}}}.

404

HardJEE Advanced2022

An ideal gas of density \rho=0.2 \mathrm{~kg} \mathrm{~m}^{-3} enters a chimney of height h at the rate of \alpha= 0.8 \mathrm{~kg} \mathrm{~s}^{-1} from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is A_{1}=0.1 \mathrm{~m}^{2} and the upper end is A_{2}=0.4 \mathrm{~m}^{2}. The pressure and the temperature of the gas at the lower end are 600 \mathrm{~Pa} and 300 \mathrm{~K}, respectively, while its temperature at the upper end is 150 \mathrm{~K}. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take g=10 \mathrm{~m} \mathrm{~s}^{-2} and the ratio of specific heats of the gas \gamma=2. Ignore atmospheric pressure. Which of the following statement(s) is(are) correct?

Options:

A) The pressure of the gas at the upper end of the chimney is 300 \mathrm{~Pa}.

B) The velocity of the gas at the lower end of the chimney is 40 \mathrm{~m} \mathrm{~s}^{-1} and at the upper end is 20 \mathrm{~ms}^{-1}.

C) The height of the chimney is 590 \mathrm{~m}.

D) The density of the gas at the upper end is 0.05 \mathrm{~kg} \mathrm{~m}^{-3}.

405

MediumJEE Advanced2021

A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle $\theta = 45^\circ. P 1 and P 2 are pressures at points 1 and 2, respectively, located at the base of the tube. Let \beta = (P 1 - P 2 )/(\rhogd), where \rho$ is density of water, d is the inner diameter of the tube and g is the acceleration due to gravity. Which of the following statement(s) is(are) correct?

Options:

A) \beta = 0 when a = g/\sqrt 2

B) \beta > 0 when a = g/\sqrt 2

C) \beta = {{\sqrt 2 - 1} \over {\sqrt 2 }}$ when a = g/2

D) \beta = {1 \over {\sqrt 2 }}$ when a = g/2

406

HardJEE Advanced2020

As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate (KMnO 4 ) of different concentrations n 1 and n 2 (n 1 > n 2 ) molecules per unit volume with $\Delta n = (n 1 − n 2 ) << n 1 . When they are connected by a tube of small length l and cross-sectional area S, KMnO 4 starts to diffuse from the left to the right vessel through the tube. Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion. The speed v of the molecules is limited by the viscous force −\beta v on each molecule, where \beta is a constant. Neglecting all terms of the order (\Delta $n) 2 , which of the following is/are correct? (k B is the Boltzmann constant)

Options:

A) the force causing the molecules to move across the tube is $\Delta n{k_b}TS

B) force balance implies ${n_1}\beta vl = \Delta n{k_B}T

C) total number of molecules going across the tube per sec is $\left( {{{\Delta n} \over l}} \right)\left( {{{{k_B}T} \over \beta }} \right)S

D) rate of molecules getting transferred through the tube does not change with time

407

HardJEE Advanced2019

A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T 1 and T 2 of different materials having water contact angles of 0$^\circ and 60^\circ $, respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in figure. Which of the following option(s) is (are) correct? [Surface tension of water = 0.075 N/m, density of water = 1000 kg/m 3 , take g = 10 m/s 2 ]

Options:

A) For case I, if the joint is kept at 8 cm above the water surface, the height of water colomn in the tube will be 7.5 cm. (Neglect the weight of the water in the meniscus).

B) For case I, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be more than 8.75 cm. (Neglect the weight of the water in the meniscus).

C) The correction in the height of water column raised in the tube, due to weight of water contained in the meniscus, will be different for both cases.

D) For case II, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be 3.75 cm. (Neglect the weight of the water in the meniscus).

408

MediumJEE Advanced2018

Consider a thin square plate floating on a viscous liquid in a large tank. The height $h of the liquid in the tank is much less than the width of the tank. The floating place is pulled horizontally with a constant velocity {\mu _{0.}}$ Which of the following statements is (are) true?

Options:

A) The resistive force of liquid on the plate is inversely proportional to $h

B) The resistive force of liquid on the plate is independent of the area of the plate

C) The tangential (shear) stress on the floor of the tank increases with ${\mu _0}

D) The tangential (shear) stress on the plate varies linearly with the viscosity $\eta $ of the liquid

409

MediumJEE Advanced2018

A uniform capillary tube of inner radius $r is dipped vertically into a beaker filled with water. The water rises to a height h in the capillary tube above the water surface in the beaker. The surface tension of water is \sigma . The angle of contact between water and the wall of the capillary tube is \theta .$ Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

Options:

A) For a given material of the capillary tube, $h decreases with increase in r

B) For a given material of the capillary tube, $h is independent of \sigma

C) If this experiment is performed in a lift going up with a constant acceleration, then $h$ decreases

D) h is proportional to contact angle \theta

410

MediumJEE Advanced2017

A human body has a surface area of approximately $1\,m{}^2. The normal body temperature is 10 K above the surrounding room temperature {T_0}. Take the room temperature to be {T_0} = 300K. For {T_0} = 300\,K, the value of \sigma T_0^4 = 460\,W{m^{ - 2}} (where \sigma $ is the Stefan-Boltzmann constant). Which of the following options is / are correct?

Options:

A) The amount of energy radiated by the body in $1 second is close to 60$ joules

B) If the surrounding temperature reduces by a small amount $\Delta {T_0} < < {T_0}, then to maintain the same body temperature the same (living) human being needs to radiate \Delta W = 4\sigma T_0^3\Delta {T_0}$ more energy per unit time

C) Reducing the exposed surface area of the body (e.g. by curling up) allows human to maintain the same body temperature while reducing the energy lost by radiation

D) If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths

411

MediumJEE Advanced2015

A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at r (r < R), then the correct option(s) is(are)

Options:

A) P(r = 0) = 0

B) {{P(r = 3R/4)} \over {P(r = 2R/3)}} = {{63} \over {80}}

C) {{P(r = 3R/5)} \over {P(r = 2R/5)}} = {{16} \over {21}}

D) {{P(r = R/2)} \over {P(r = R/3)}} = {{20} \over {27}}

412

MediumJEE Advanced2015

In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then, the correct statements is/are

Options:

A) P has more tensile strength than Q

B) P is more ductile than Q

C) P is more brittle than Q

D) The Young's modulus of P is more than that of Q

413

MediumJEE Advanced2015

Two spheres P and Q for equal radii have densities $\rho 1 and \rho 2 , respectively. The spheres are connected by a massless string and placed in liquids L 1 and L 2 of densities \sigma 1 and \sigma 2 and viscosities {\eta _1} and {\eta _2}$, respectively. They float in equilibrium with the sphere P in L 1 and sphere Q in L 2 and the string being taut (see figure) If sphere P along in L 2 has terminal velocity v P and Q alone in L 1 ha terminal velocity v Q , then

Options:

A) {{|{v_P}|} \over {|{v_Q}|}} = {{{\eta _1}} \over {{\eta _2}}}

B) {{|{v_P}|} \over {|{v_Q}|}} = {{{\eta _2}} \over {{\eta _1}}}

C) v P . v Q > 0

D) v P . v Q < 0

414

MediumJEE Advanced2014

Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5 kg water by 40 K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40 K?

Options:

A) 4, if wires are in parallel

B) 2, if wires are in series

C) 1, if wires are in series

D) 0.5, if wires are in parallel

415

EasyJEE Advanced2013

A solid sphere of radius R and density $\rho is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3\rho . The complete arrangement is placed in a liquid of density 2\rho $ and is allowed to reach equilibrium. The correct statement(s) is (are)

Options:

A) The net elongation of the spring is ${{4\pi {R^3}\rho g} \over {3k}}

B) The net elongation of the spring is ${{8\pi {R^3}\rho g} \over {3k}}

C) The light sphere is partially submerged

D) The light sphere is completely submerged

416

EasyJEE Advanced2012

A person blows into the open end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,

Options:

A) a high-pressure pulse starts travelling up the pipe, if the other end of the pipe is open.

B) a low-pressure pulse starts travelling up the pipe, it the other end of the pipe is open.

C) a low-pressure pulse starts travelling up the pipe, if the other end of the pipe is closed.

D) a high-pressure pulse starts travelling up the pipe, if the other end of the pipe is closed.

417

EasyJEE Advanced2011

A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat Q flows only from left to right through the blocks. Then, in steady-state

Options:

A) heat flow through A and E slabs are same.

B) heat flow through slab E is maximum.

C) temperature difference across slab E is smallest.

Options:

A) {{4P{{(T(t) - {T_0})}^4}} \over {{\beta ^4}T_0^5}}

B) {{4P{{(T(t) - {T_0})}^3}} \over {{\beta ^4}T_0^4}}

C) {{4P(T(t) - {T_0})} \over {{\beta ^4}T_0^2}}

D) {{4P{{(T(t) - {T_0})}^2}} \over {{\beta ^4}T_0^3}}

434

MediumJEE Advanced2014

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance d of 1.2 m from the person. In the following, state of the lift’s motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer using the options given below the lists. List - I List - II P. Lift is accelerating vertically up. 1. d=1.2 m Q. Lift is accelerating vertically down with an acceleration less than the gravitational acceleration. 2. d > 1.02 m R. Lift is moving vertically up with constant speed. 3 . d < 1.2 m S. Lift is falling freely. 4. No water leaks out of the jar

Options:

A) P - 2, Q - 3, R - 2, S - 4

B) P - 2, Q - 3, R - 1, S - 4

C) P - 1, Q - 1, R - 1, S - 4

D) P - 2, Q - 3, R - 1, S - 1

435

MediumJEE Advanced2014

A glass capillary tube is of the shape of truncated cone with an apex angle $\alpha so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height h, where the radius of its cross section is b. If the surface tension of water is S, its density is \rho, and its contact angle with glass is \theta$, the value of h will be (g is the acceleration due to gravity)

Options:

A) {{2S} \over {b\rho g}}\cos (\theta - \alpha )

B) {{2S} \over {b\rho g}}\cos (\theta + \alpha )

C) {{2S} \over {b\rho g}}\cos (\theta - \alpha /2)

D) {{2S} \over {b\rho g}}\cos (\theta + \alpha /2)

436

EasyJEE Advanced2014

A spray gun is shown in the below figure where a piston pushes air out of a nozzle. A thin tube of uniform cross-section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm, respectively. The upper end of the container is open to the atmosphere.

Options:

A) 0.1 \mathrm{~ms}^{-1}

B) 1 \mathrm{~ms}^{-1}

C) 2 \mathrm{~ms}^{-1}

D) 8 \mathrm{~ms}^{-1}

437

MediumJEE Advanced2014

A spray gun is shown in the below figure where a piston pushes air out of a nozzle. A thin tube of uniform cross-section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm, respectively. The upper end of the container is open to the atmosphere.

Options:

A) \sqrt{\frac{\rho_a}{\rho_{\ell}}}

B) \sqrt{\rho_a \rho_{\ell}}

C) \sqrt{\frac{\rho_{\ell}}{\rho_a}}

D) \rho_{\ell}

438

MediumJEE Advanced2013

One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

Options:

A) 0.25

B) 0.50

C) 2.00

D) 4.00

439

MediumJEE Advanced2012

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If ${\rho _c}$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

Options:

A) more than half-filled if ${\rho _c}$ is less than 0.5.

B) more than half-filled if ${\rho _c}$ is more than 1.0.

C) half-filled if ${\rho _c}$ is more than 0.5.

D) less than half-filled if ${\rho _c}$ is less than 0.5.

440

MediumJEE Advanced2010

When liquid medicine of density $\rho $ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When the force becomes smaller than the weight of the drop, the drop gets detached from the dropper. After the drop detaches, its surface energy is

Options:

A) 1.4 $ \times $ 10 −6 J

B) 2.7 $ \times $ 10 −6 J

C) 5.4 $ \times $ 10 −6 J

D) 8.1 $ \times $ 10 −6 J

441

MediumJEE Advanced2010

When liquid medicine of density $\rho is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When the force becomes smaller than the weight of the drop, the drop gets detached from the dropper. If r = 5 \times 10 −4 m, \rho $ = 10 3 kg m −3 , g = 10 m/s 2 , T = 0.11 Nm −1 , the radius of the drop when it detaches from the dropper is approximately

Options:

A) 1.4 $ \times $ 10 −3 m

B) 3.3 $ \times $ 10 −3 m

C) 2.0 $ \times $ 10 −3 m

D) 4.1 $ \times $ 10 −3 m

442

MediumJEE Advanced2010

When liquid medicine of density $\rho is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When the force becomes smaller than the weight of the drop, the drop gets detached from the dropper. If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r$ << R) is

Options:

A) 2\pi rT

B) 2\pi RT

C) {{2\pi {r^2}T} \over R}

D) {{2\pi {R^2}T} \over r}

443

MediumJEE Advanced2008

A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,

Options:

A) air from end 1 flows towards end 2. No change in the volume of the soap bubbles

B) air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases

C) no change occurs

D) air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases

444

EasyJEE Advanced2008

STATEMENT - 1 : The stream of water flowing at high speed from a garden hose pipe tends to spread line a fountain when held vertically up, but tends to narrow down when held vertically down. and STATEMENT - 2 : In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

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

445

EasyJEE Advanced2008

A small spherical monoatomic ideal gas bubble $\left( {\gamma = {5 \over 3}} \right) is trapped inside a liquid of density \rho_1 (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T_0, the height of the liquid is H and the atmospheric pressure is P_0$ (Neglect surface tension)

Options:

A) Only the force of gravity

B) The force due to gravity and the force due to the pressure of the liquid

C) The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid

D) The force due to gravity and the force due to viscosity of the liquid

446

MediumJEE Advanced2008

A small spherical monoatomic ideal gas bubble $\left( {\gamma = {5 \over 3}} \right) is trapped inside a liquid of density \rho_1 (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T_0, the height of the liquid is H and the atmospheric pressure is P_0$ (Neglect surface tension)

Options:

A) {T_0}{\left( {{{{P_0} + {\rho _l}gH} \over {{P_0} + {\rho _l}gy}}} \right)^{{2 \over 5}}}

B) {T_0}{\left( {{{{P_0} + {\rho _l}g(H - y)} \over {{P_0} + {\rho _l}gH}}} \right)^{{2 \over 5}}}

C) {T_0}{\left( {{{{P_0} + {\rho _l}gH} \over {{P_0} + {\rho _l}gy}}} \right)^{{3 \over 5}}}

D) {T_0}{\left( {{{{P_0} + {\rho _l}g(H - y)} \over {{P_0} + {\rho _l}gH}}} \right)^{{3 \over 5}}}

447

HardJEE Advanced2008

A small spherical monoatomic ideal gas bubble $\left( {\gamma = {5 \over 3}} \right) is trapped inside a liquid of density \rho_1 (see figure). Assume that the bubble does not exchange any heat with the liquid. The bubble contains n moles of gas. The temperature of the gas when the bubble is at the bottom is T_0, the height of the liquid is H and the atmospheric pressure is P_0$ (Neglect surface tension)

Options:

A) {\rho _l}nRg{T_0}{{{{({P_0} + {\rho _l}gH)}^{{2 \over 5}}}} \over {{{({P_0} + {\rho _l}gy)}^{{7 \over 5}}}}}

B) {{{\rho _l}nRg{T_0}} \over {{{({P_0} + {\rho _l}gH)}^{{2 \over 5}}}{{[{P_0} + {\rho _l}g(H - y)]}^{{3 \over 5}}}}}

C) {\rho _l}nRg{T_0}{{{{({P_0} + {\rho _l}gH)}^{{3 \over 5}}}} \over {{{({P_0} + {\rho _l}gy)}^{{8 \over 5}}}}}

D) {{{\rho _l}nRg{T_0}} \over {{{({P_0} + {\rho _l}gH)}^{{3 \over 5}}}[{P_0} + {\rho _l}g{{(H - y)}^{{2 \over 5}}}}}

448

MediumJEE Advanced2007

Water is filled up to a height $h in a beaker of radius R as shown in the figure. The density of water is \rho, the surface tension of water is T and the atmospheric pressure is P. Consider a vertical section A B C D$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

Options:

A) \left|2 \mathrm{P}_{0} \mathrm{Rh}+\pi \mathrm{R}^{2} \rho g h-2 \mathrm{RT}\right|

B) \left|2 \mathrm{P}_{0} \mathrm{Rh}+\pi \mathrm{R \rho gh}^{2}-2 \mathrm{RT}\right|

C) \left|P_{0} \pi R^{2}+R \rho g h^{2}-2 R T\right|

D) \left|\mathrm{P}_{0} \mathrm{R}^{2}+\mathrm{R} \rho g \mathrm{~h}^{2}+2 \mathrm{RT}\right|

449

EasyJEE Advanced2007

Column I gives some devices and Column II gives some process on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS. Column I Column II (A) Bimetallic strip (P) Radiation from a hot body (B) Steam engine (Q) Energy conversion (C) Incandescent lamp (R) Melting (D) Electric fuse (S) Thermal expansion

Options:

A) [\mathrm{A} \rightarrow(\mathrm{Q, S}); \mathrm{B} \rightarrow(\mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{R})]

B) [\mathrm{A} \rightarrow(\mathrm{R, S}); \mathrm{B} \rightarrow(\mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{R, S})]

C) [\mathrm{A} \rightarrow(\mathrm{S}); \mathrm{B} \rightarrow(\mathrm{Q}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{R})]

D) [\mathrm{A} \rightarrow(\mathrm{P, S}); \mathrm{B} \rightarrow(\mathrm{R}); \mathrm{C} \rightarrow(\mathrm{P}); \mathrm{D} \rightarrow(\mathbf{R})]

450

MediumJEE Advanced2006

A wooden cylinder of diameter 4 r, height h and density \frac{\rho}{3} is kept on a hole of diameter 2 r of a tank, filled with water of density \rho as shown in the figure. The height of the base of cylinder from the base of tank is H .

Options:

A) \frac{2 h}{3}

B) \frac{5 h}{4}

C) \frac{5 h}{3}

D) \frac{5 h}{2}

451

MediumJEE Advanced2006

A wooden cylinder of diameter 4 r, height h and density \frac{\rho}{3} is kept on a hole of diameter 2 r of a tank, filled with water of density \rho as shown in the figure. The height of the base of cylinder from the base of tank is H .

Options:

A) \frac{h}{3}

B) \frac{4 h}{9}

C) \frac{2 h}{3}

D) h

452

MediumJEE Advanced2006

A wooden cylinder of diameter 4 r, height h and density \frac{\rho}{3} is kept on a hole of diameter 2 r of a tank, filled with water of density \rho as shown in the figure. The height of the base of cylinder from the base of tank is H .

Options:

A) cylinder will not move up and remains at its position.

B) for h_2=\frac{h}{3}, the cylinder again starts moving up

C) for h_2=\frac{h}{4}, the cylinder again starts moving up

D) for h_2=\frac{h}{5}, the cylinder again starts moving up.

453

MediumJEE Advanced2005

A U-tube is rotated about one of its limbs with an angular velocity $\omega. Find the difference in height \mathrm{H} of the liquid (density \rho ) level, where the diameter of the tube is d < <\mathrm{L}$.

Options:

A) \mathrm{H=\omega^2L^2/2g}

B) \mathrm{H=\omega^2L^2/3g}

C) \mathrm{H=5\omega^2L^2/2g}

D) \mathrm{H=\omega^2L^2/g}

453

Total Questions

119

Easy

326

Medium

Hard

Study Tips

Before You Start

• Review the chapter concepts thoroughly
• Keep a notebook for important formulas
• Practice similar problems from your textbook
• Time yourself to improve speed

After Practice

• Review all incorrect answers carefully
• Watch video solutions for difficult questions
• Make notes of common mistakes
• Practice similar questions again later