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 about their own symmetry axes. The amounts of work (W) required to bring them to res

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Solution

Q.
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 [2018]

1 $W_{C} > W_{B} > W_{A}$

2 $W_{A} > W_{B} > W_{C}$

3 $W_{B} > W_{A} > W_{C}$

4 $W_{A} > W_{C} > W_{B}$

Ans.
(1)

Work done required to bring an object to rest

$Δ W = Δ K E$

$Δ W = \frac{1}{2} I ω^{2} where I = moment of inertia$

For same $ω,$ $Δ W \propto I$

$For a solid sphere, I_{A} = \frac{2}{5} M R^{2}$

$For a thin circular disk, I_{B} = \frac{1}{2} M R^{2}$

$For a circular ring, I_{C} = M R^{2}$

$∴$ $I_{C} > I_{B} > I_{A}$ $∴$ $W_{C} > W_{B} > W_{A}$

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