A child with mass \( m \) is standing at the edge of a merry go round having moment of inertia \...

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A child with mass \( m \) is standing at the edge of a merry go round having 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 tangential velocity \( v \) with respect to the ground. The new angular velocity of the merry go round is
(a) \( \sqrt{\frac{I \omega^{2}-m v^{2}}{I}} \)
(b) \( \sqrt{\frac{\left(I+m R^{2}\right) \omega^{2}-m v^{2}}{I}} \)
(c) \( \frac{I \omega-m v R}{I} \)
(d) \( \frac{\left(I+m R^{2}\right) \omega-m v R}{I} \)
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