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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
$W_C>W_B>W_A$
$W_A>W_B>W_C$
$W_A>W_C>W_B$
$W_B>W_A>W_C$
Solution
Work done required to bring a object to rest $\Delta W = \Delta KE$
$\begin{array}{l}
\Delta W = \frac{1}{2}I{\omega ^2}\,;\,where\,I\, = moment\,of\,inertia\\
For\,same\,\omega ,\,\Delta W \propto I\\
For\,a\,solid\,sphere,\,{I_A} = \frac{2}{5}M{R^2}\\
For\,a\,thin\,cicular\,disk,\,{I_B} = \frac{1}{2}M{R^2}\\
For\,a\,circular\,ring,\,{I_c} = M{R^2}\\
\therefore \,\,{I_c} > {I_B} > {I_A}\,\,\therefore \,\,{W_c} > {W_B} > {W_A}
\end{array}$
