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A cockroach is moving with velocity \( v \) in anticlockwise direction on the rim of a disc of radius \( R \) of mass \( m \). The moment of inertia of the disc about the axis is \( I \) and it is rotating in clockwise direction with an angular velocity \( \omega \). If the cockroach stops, the angular velocity of the disc will be
[DCE 2006]
(a) \( \frac{I \omega}{I+m R^{2}} \)
(b) \( \frac{I \omega+m v R}{I+m R^{2}} \)
(c) \( \frac{I \omega-m v R}{I+m R^{2}} \)
(d) \( \frac{I \omega-m u R}{I} \)
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