A child with mass \( m \) is standing at the edge of a disc with moment of inertia I, radius \( \mathrm{R} \), and initial
\( \mathrm{P} \) angular velocity \( \omega \). See figure given below. The child jumps off the edge of the disc with
W tangential velocity \( v \) with respect to the ground. The new angular velocity of the disc is
(1) \( \sqrt{\frac{I \omega^{2}-m v^{2}}{I}} \)
(2) \( \sqrt{\frac{\left(1+m R^{2}\right) \omega^{2}-m v^{2}}{I}} \)
(3) \( \frac{I \omega-m v R}{I} \)
(4) \( \frac{\left(I+m R^{2}\right) \omega-m v R}{I} \)
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