A ring of radius 0.5, m and mass 10 ,kg is rotating about its diameter with an angular velocit

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6.System of Particles and Rotational Motion

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A ring of radius $0.5\, m$ and mass $10 \,kg$ is rotating about its diameter with an angular velocity of $20 \,rad/s.$ Its kinetic energy is .......... $J$

A

$10$

B

$100$

C

$500$

D

$250$

Solution

Rotational kinetic energy $\frac{1}{2}I{\omega ^2}$

$= \frac{1}{2}\left( {\frac{1}{2}M{R^2}} \right)\,{\omega ^2}$

$ = \frac{1}{2}\left( {\frac{1}{2} \times 10 \times {{(0.5)}^2}} \right)\,{\left( {20} \right)^2}$

$= 250\,J$

Standard 11

Physics

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