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Question

# The moment of inertia of a solid cylinder about its axis is given by 1/2MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is:

A
1:1
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B
2:2
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C
1:2
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D
1:3
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Solution

## The correct option is C 1:2The rotational kinetic energy is given byRE=12Iω2The transnational kinetic energy is given byTE=12Mv2 Now,RETE=12Iω212Mv2RETE=Iω2v2Since, I=12MR2 ........givenHence,RETE=(12MR2)ω2Mv2using, ω=vR in above equation, we getRETE=(12R2)(vR)2v2RETE=12

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