SATHEE: Rotational Motion Question 98

Rotational Motion Question 98

Question: A solid sphere of mass $(M)$ and radius $(R)$ is rotating about its axis with a constant angular velocity $(ω)$ . If the radius of the sphere is halved, what will be the new angular velocity?

Options:

A) $ω$

B) $\frac{ω}{2}$

C) $\frac{ω}{4}$

D) $2 ω$

Show Answer

Answer:

Correct Answer: D

Solution:

The moment of inertia (I) of a solid sphere about its axis is given by $(\frac{2}{5} M R^{2})$ .

According to the conservation of angular momentum $(L = I ω = constant)$ , if the radius is halved, the new moment of inertia $(I^{'})$ becomes $(\frac{2}{5} M$ $(\frac{R}{2})^{2} = \frac{1}{5} M R^{2})$ .

Therefore, the new angular velocity $(ω^{'})$ must be such that $(I^{'} ω^{'} = I ω)$ .

Therefore, $(\frac{1}{5} M R^{2} ω^{'}$ = $\frac{2}{5} M R^{2} ω)$

Solving for $(ω^{'})$ , we get $(ω^{'} = 2 ω)$ .

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Rotational Motion Question 98

Question: A solid sphere of mass (M) and radius (R) is rotating about its axis with a constant angular velocity (ω). If the radius of the sphere is halved, what will be the new angular velocity?

Options:

Answer:

Solution:

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Question: A solid sphere of mass $(M)$ and radius $(R)$ is rotating about its axis with a constant angular velocity $(ω)$ . If the radius of the sphere is halved, what will be the new angular velocity?