Q.

A solid sphere of mass ‘M’ and radius ‘R’ is initially at rest. Solid sphere is gradually lowered onto a truck moving with constant velocity V0.

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The final speed of sphere’s centre of mass in ground frame when eventually pure rolling sets is (in multiples of V07) ?

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answer is 2.

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Detailed Solution

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v = velocity of centre of sphere wrt truck

Applying conservation of angular momentum about point P on the truck:

MV0R=MvR+Iω=MvR+25MR2ω  .....(1)

for pure rolling, v=ωR .... (2)

solving (1) and (2),

v=57V0

velocity wrt ground:

v'=V0-v=27V0

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