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# I have a doubt, kindly clarify. - Motion of System Of Particles and Rigid Body - NEET

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

• Option 1)

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

• Option 2)

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

• Option 3)

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

• Option 4)

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

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As we have learned

Kinetic energy of rotation -

$K=\frac{1}{2}Iw^{2}$

- wherein

$I$ = moment of inertia about axis of rotation

$w$ = angular velocity

work energy theorem states that work done =change in kinetic energy

$=\frac{1}{2}IW^{2}$

$I_{c}> I_{B}> I_{A}$

$\therefore K\cdot E_{c}> K\cdot E_{B}> K\cdot E_{A}$

$W_{c}> W_{B}> W_{A}$

Option 1)

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

This is incorrect

Option 2)

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

This is incorrect

Option 3)

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

This is correct

Option 4)

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

This is incorrect

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