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NEET Medium

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

1

WB>WA>WCW_B > W_A > W_C

2

WA>WB>WCW_A > W_B > W_C

3

WC>WB>WAW_C > W_B > W_A

4

WA>WC>WBW_A > W_C > W_B

Step-by-Step Solution

Work done required to bring them to rest is ΔW=ΔKE=12Iω2\Delta W = \Delta KE = \frac{1}{2} I \omega^2. Since ω\omega is same, ΔW∝I\Delta W \propto I. The moments of inertia are IA=25MR2I_A = \frac{2}{5}MR^2, IB=12MR2I_B = \frac{1}{2}MR^2, IC=MR2I_C = MR^2. Thus, WA:WB:WC=25:12:1=4:5:10W_A : W_B : W_C = \frac{2}{5} : \frac{1}{2} : 1 = 4 : 5 : 10. Therefore, WC>WB>WAW_C > W_B > W_A.

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