Three objects, A : (a solid sphere), B : (a thin circular disk) a… - Vidyadip

MCQ

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

A
$W_C>W_B>W_A$
B
$W_A>W_B>W_C$
C
$W_A>W_C>W_B$
D
$W_B>W_A>W_C$

✓

Answer

Work done required to bring a object to rest $\Delta W=\Delta K E$
$\Delta W=\frac{1}{2} I \omega^2 ;$ 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, $I_c=M R^2$
$\therefore I_c>I_B>I_A \therefore W_c>W_B>W_A$

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