Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same

Question

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

Accepted Answer

Work done required to bring them to rest is $\Delta W = \Delta KE = \frac{1}{2} I \omega^2$. Since $\omega$ is same, $\Delta W \propto I$. The moments of inertia are $I_A = \frac{2}{5}MR^2$, $I_B = \frac{1}{2}MR^2$, $I_C = MR^2$. Thus, $W_A : W_B : W_C = \frac{2}{5} : \frac{1}{2} : 1 = 4 : 5 : 10$. Therefore, $W_C > W_B > W_A$.

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