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Question

A child with mass m is standing at the edge of a merry-go-round (A large uniform disc which rotates in horizontal plane about a fixed vertical axis in parks) with moment of inertia I, radius R, and initial angular velocity as shown in figure.The child jumps off the edge of the merry-go-round with a velocity v with respect to the ground in direction tangent to periphery of the disc as shown.The new angular velocity of the merry-go-round is:
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A
Iω2mv2I
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B
(I+mR2)ω2mv2I
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C
IωmvRI
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D
(I+mR2)ωmvRI
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Solution

The correct option is D (I+mR2)ωmvRI
Let the angular momentum of the disc after the child jumps off is ω
Let I be the MI of the disc. The MI of the child is mR2 where m is the mass of the child.
(I+mR2)ω=mvR+Iω
ω=(I+mR2)ωmvRI

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