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System Of Particles And Rotational Motion

Question

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

W_C > W_B> W_A

W_A > W_B > W_C

W_A>W_C>W_B

W_B>W_A>W_C

Solution

W_C > W_B> W_A

W_A > W_B > W_C

Work done required to bring them rest

$∆ W = ∆ K E ∆ W = \frac{1}{2} I ω^{2} ∆ W \propto I f o r s a m e ω W_{A} : W_{B} : W_{C} = \frac{2}{5} M R^{2} : \frac{1}{2} M R^{2} : M R^{2} = \frac{2}{5} : \frac{1}{2} : 1 = 4 : 5 : 10 \Rightarrow W_{C} > W_{B} > W_{A}$

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System Of Particles And Rotational Motion

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