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A solid uniform sphere rotating about its axis (with rotational kinetic energy ω0) is placed on a rough horizontal plane without any translational push. Friction coefficient p is not same everywhere on the plane and it may differ even at each point. After sometime the sphere begins pure rolling with total kinetic energy E. Then:

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a

ω=2ω0/5

b

ω=2ω0/7

c

ω=5ω0/7

d

ω cannot be expressed in terms ω0

answer is B.

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Detailed Solution

Li = Lf⇒ 25MR2ω0=MVR+25MR2ω= ω=27ω0TKEi=1225MR2ω02;TKEf=12mv2+12Iω2=710Mω2R2=235MR2ω02

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A solid uniform sphere rotating about its axis (with rotational kinetic energy ω0) is placed on a rough horizontal plane without any translational push. Friction coefficient p is not same everywhere on the plane and it may differ even at each point. After sometime the sphere begins pure rolling with total kinetic energy E. Then: