Question 205: Work, Energy and Power & Circular Motion

Question

A weightless thread can bear tension up to 3.7 kg wt. A stone of mass 500 gram is tied to it and revolved in circular path of radius 4 m in vertical plane. Maximum angular velocity of the stone will be (acceleration due to gravity, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

Accepted Answer

Given:
Maximum tension in thread, $T_{	ext{max}} = 3.7~	ext{kg wt} = 3.7 	imes 10~	ext{N} = 37~	ext{N}$
Mass of stone, $m = 500~	ext{g} = 0.5~	ext{kg}$
Radius of circle, $r = 4~	ext{m}$
Acceleration due to gravity, $g = 10~	ext{m/s}^2$
Step 1: Identify the location of maximum tension
In the vertical circular motion, the tension will be maximum at the
lowest point
.
Step 2: Write the equation for tension at the lowest point
At the lowest point,
$$ T_{	ext{max}} = m \omega^2 r + mg $$
Where,
$m \omega^2 r$ is the centripetal force,
$mg$ is the weight (acting downwards).
Step 3: Substitute the given values
$$ 37 = 0.5 \omega^2 	imes 4 + 0.5 	imes 10 $$
$$ 37 = 2 \omega^2 + 5 $$
Step 4: Solve for $\omega$
Subtract $5$ from both sides:
$$ 37 - 5 = 2 \omega^2 $$
$$ 32 = 2 \omega^2 $$
$$ \omega^2 = \frac{32}{2} = 16 $$
$$ \omega = \sqrt{16} = 4~	ext{rad/s} $$
Answer:
Option B
($4~	ext{rad/s}$) is correct.

Answer

$16 \mathrm{rad} / \mathrm{s}$

Answer

$4 \mathrm{rad} / \mathrm{s}$

Answer

$2 \mathrm{rad} / \mathrm{s}$

Answer

$8 \mathrm{rad} / \mathrm{s}$

Work, Energy and Power & Circular Motion

A weightless thread can bear tension up to 3.7 kg wt. A stone of mass 500 gram is tied to it and revolved in circular path of radius 4 m in vertical plane. Maximum angular velocity of the stone will be (acceleration due to gravity, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 )

Choose the correct answer: