A cord is wound round the circumference of a solid cylinder of radius \( R \) and mass \( M \). ...

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A cord is wound round the circumference of a solid cylinder of radius \( R \) and mass \( M \). The axis of the cylinder is horizontal. \( A \) weight \( m g \) is attached to the end of the cord and falls from rest. After falling through a distance \( h \).
The angular velocity of the cylinder will be
(1) \( \frac{2 m g}{M+2 m} \)
(2) \( \sqrt{\frac{2 g h}{R^{2}}} \)
(3) \( \sqrt{\frac{4 m g h}{(M+2 m) R^{2}}} \)
(4) \( \sqrt{\frac{4 m g h}{M+2 m}} \)
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