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Moment of Inertia of a Disc

Three objects...

Question

Three objects $A$ (solid sphere), $B$ (thin circular disk) and $C$ (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

A

W_{B} > W_{A} > W_{C}

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B

W_{C} > W_{B} > W_{A}

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C

W_{A} > W_{C} > W_{B}

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D

W_{A} > W_{B} > W_{C}

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Solution

The correct option is B $W_{C} > W_{B} > W_{A}$
Work done is change in kinetic energy.
hence more the kinetic energy, more will be the work done.
$K . E . = \frac{I w^{2}}{2}$
They all have same angular velocity.
Hence more the moment of inertia, more the kinetic energy and hence more will be the work done.
Hence, $W_{C} > W_{B} > W_{A}$

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