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- A child with mass \( m \) is standing at the edge of a playground merry-go-round (A large uniform disc which rotates in
P horizontal plane about a fixed vertical axis in parks) with

W moment of inertia \( I \), radius \( R \), and initial angular velocity \( \omega \) as shown in the 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
(1) \( \sqrt{\frac{I \omega^{2}-m v^{2}}{I}} \)
(3) \( \frac{I \omega-m v R}{I} \)
(2) \( \sqrt{\frac{\left(I+m R^{2}\right) \omega^{2}-m v^{2}}{I}} \)
(4) \( \frac{\left(I+m R^{2}\right) \omega-m v R}{I} \)
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