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Question

A hollow spherical ball rolls on a table without slipping. Ratio of its rotational kinetic energy to its total kinetic energy is


A
5:2
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B
2:7
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C
2:5
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D
7:2
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Solution

The correct option is C 2:5
In case of pure rolling, body will have K.ETrans as well as K.ERot.
v=Rω ...(i) for pure rolling,

where vvCM of spherical ball.
Moment of inertia of hollow sphere about axis passing through its COM is:
ICM=23mr2
K.ETrans=12mv2
K.ERot=12ICMω2
Hence total kinetic energy of ball is:
K.ETotal=K.ETrans+K.ERot ...(ii)
From Eq (i),
K.ERot=12(23 mr2)ω2=13m(rω)2
K.ERot=13mv2
From Eq. (ii),
K.ETotal=12mv2+13mv2=56mv2
K.ERotK.ETotal=13mv256mv2=25
K.ERot:K.ETotal=2:5


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