System of Particles and Rotational Motion - Result Question 74
81. 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
[2018]
(a) W $ _{C}>W_B>W_A$
(b) $W_A>W_B>W_C$
(c) $W_A>W_C>W_B$
(d) $W_B>W_A>W_C$
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Answer:
Correct Answer: 81. (a)
Solution:
- (a) Work done required to bring them rest $\Delta W=\Delta KE$ (work-energy theorem) $\Delta W=\frac{1}{2} I \omega^{2}(\Delta k E _{\text{rot }}=\frac{1}{2} I \omega^{2})$
or, $\Delta W \propto I($ for same $\omega)$
$ \begin{aligned} & I _{\text{solid sphere }}=\frac{2}{5} M R^{2}, I _{\text{Disk }}=\frac{1}{2} M R^{2} \\ & I _{\text{Ring }}=MR^{2} \quad \therefore \quad W_C>W_B>W_A \end{aligned} $
