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Q.

When a uniform solid sphere of mass M rolls without slipping from rest down an inclined plane such that its centre of mass descends through a height h, its translational kinetic energy will be

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a

mgh

b

57mgh

c

27mgh

d

mgh2

answer is B.

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Detailed Solution

K=12mV2+12Iω2=mgh 12mV2+1225mV2=mgh          I=25mR2,ω=VR12mV275=mghK=12mV2=57mgh
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When a uniform solid sphere of mass M rolls without slipping from rest down an inclined plane such that its centre of mass descends through a height h, its translational kinetic energy will be