Rotational Motion Question 209

Question: A child with mass m is standing at the edge of a playground merry-go-round (A large uniform disc which rotates in horizontal plane about a fixed vertical axis in parks) with moment of inertia Vs I, radius R, and initial angular velocity w. 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 veloity of the merry-go-round is :

Options:

A) Iω2mv2I

B) (I+mR2)ω2mv2I

C) IωmvRI

D) (IωmR2)ωmvRI

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Answer:

Correct Answer: D

Solution:

[d] Let the angular velocity of disc after child jumps off.

be ω

From conservation of angular momentum (I+mR2)ω=mvR+Iω.

ω=(I+mR2)ω+mvRI



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