A horizontal turn table in the form of a disc of radius \( r \) carries a gun at \( G \) and rot...

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A horizontal turn table in the form of a disc of radius \( r \) carries a gun at \( G \) and rotates with angular velocity \( \omega_{0} \) about
\( \mathrm{P} \) a vertical axis passing through the centre \( O \). The increase in

W angular velocity of the system if the gun fires a bullet of mass \( m \) with a tangential velocity \( v \) with respect to the gun is (moment of inertia of gun \( + \) table about \( O \) is \( \left.I_{0}\right) \)
(1) \( \frac{m v r}{I_{0}+m r^{2}} \)
(2) \( \frac{2 m v r}{I_{0}} \)
(3) \( \frac{v}{2 r} \)
(4) \( \frac{m v r}{2 I_{0}} \)
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