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  4. 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 to about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation

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Q. 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 to about their own symmetry axes. The amounts of work $(W)$ required to bring them to rest, would satisfy the relation

NEETNEET 2018System of Particles and Rotational Motion

Solution:

Work done required to bring them rest
$\Delta W = \Delta KE$
$ \Delta W = \frac{1}{2}I\omega^{2} $
$\Delta W \propto I $ for same $\omega$
$W_{A } : W_{B} : W_{C} = \frac{2}{5} MR^{2} : \frac{1}{2} MR^{2} : MR^{2}$
$ = \frac{2}{5} : \frac{1}{2} : 1 $
$= 4 : 5 : 10$
$ \Rightarrow W_{C} > W_{B } > W_{A} $