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Question

A ring of radius $$0.5$$ mass $$10 kg$$ is rotating about its diameter with angular velocity of $$ 20\, rad\, s^{-1} $$. Its kinetic energy is :


A
10J
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B
100J
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C
500J
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D
250J
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Solution

The correct option is D $$250 \,J$$
Moment of inertia of a ring about its diameter 
$$ I = \dfrac {1}{2} mr^2 $$
and kinetic energy is given by
$$ E_K = \dfrac {1}{2} I \omega^2 $$
$$ E_k = \dfrac {1}{4} mr^2 \omega^2 $$
$$ = \dfrac {1}{4} \times 10 \times (0.5)^2 \times (20)^2 $$
$$= 250\, J$$

Physics

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