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Question

A solid spherical ball is rolling without slipping on an inclined plane. The fraction of its total kinetic energy associated with rotation is

A
25
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B
27
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C
35
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D
37
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Solution

The correct option is B 27
Given ball is rolling without slipping, hence v=ωR
where, v= linear velocity of the ball
ω= angular velocity of the ball
Total kinetic energy = Translational Kinetic Energy + Rotational Kinetic Energy
T.K.E=12mv2+12Iω2
Here, Icom=25mR2
T.K.E=12mv2+12(25mR2)×(vR)2
T.K.E=12mv2+15mv2
T.K.E=710mv2
Rotational KE=12Iω2
=12(25mv2)×(vR)2=15mv2
Rotational K.ETotal K.E=15mv2710mv2=27

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