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Question

If a solid sphere of mass 1 kg and radius 0.1 m rolls without slipping at a uniform velocity of 1 m/s along a straight line on a horizontal floor, then its kinetic energy is

A
75 J
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B
25 J
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C
710 J
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D
1 J
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Solution

The correct option is C 710 J
When a body is in state of pure rolling the condition which hold is (v=rω) and it has translational K.E as well as rotational K.E
K.Etotal=K.ETrans+K.ERot=12mv2CM+12ICMω2 ....(i)
Where v=vCM, ω=vr and ICM=25mr2 for solid sphere.
From Eq. (i),
K.Etotal=12mv2+[12(25mr2)×v2r2]
K.Etotal=12mv2+15mv2=710mv2
K.Etotal=710×1×12=710 J

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