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Q.

Assertion: The total kinetic energy of a rolling solid sphere is the sum of translational and rotational
kinetic energies.
Reason: For all solid bodies, total kinetic energy is always twice of translational kinetic energy. [AIIMS 2017] 

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a

Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

b

Both Assertion and Reason are incorrect.

c

Assertion is correct but Reason is incorrect.

d

 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

answer is C.

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Detailed Solution

The kinetic energy of a rolling solid sphere  

=Ktrans +Krot =12mv2+12Iω2

=12mv2+12×25mR2ω2

=12mv2+15mv2     ω=vR

=7/10mv2

Hence, total kinetic energy is sum of translation and rotational kinetic energies.

For different solid bodies, total kinetic energy is not always twice of translation kinetic energy. Hence,  Assertion is correct but Reason is incorrect.

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