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

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

Answer 1

The Correct Option is B

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} $