Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation (a) WC > WB > WA (b) WA > WB > WC (c) WB > WA > WC (d) WA > WC > WB

Answer: (a). Work to stop = initial KE = 1/2Iω², so W ∝ I (same ω). IA = 2/5MR², IB = 1/2MR², IC = MR² IC > IB > IA ⇒ WC > WB > WA So the answer is (a) WC > WB > WA.

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Q46NEET 2018Medium

Rotational Kinetic Energy, Work & Power

Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed $\omega$ about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

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Answer: (a)

Work to stop = initial KE $= \frac{1}{2}I\omega^2$ , so $W \propto I$ (same $\omega$ ).
$I_A = \frac{2}{5}MR^2$ , $I_B = \frac{1}{2}MR^2$ , $I_C = MR^2$
$I_C > I_B > I_A \Rightarrow W_C > W_B > W_A$
So the answer is (a) $W_C > W_B > W_A$ .

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