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Consider two masses with \( m_{1}m_{2} \) connected by a light inextensible string that passes over a pulley of radius \( R \) and moment of inertia \( I \) about its axis of rotation. The string does not slip on the pulley and the pulley turns without friction. The two masses are released from rest separated by a vertical distance \( 2 h \). When the two masses pass each other, the speed of the masses is proportional to[KVPY 2016]
(a) \( \sqrt{\frac{m_{1}-m_{2}}{m_{1}+m_{2}+\frac{I}{R^{2}}}} \)
(b) \( \sqrt{\frac{\left(m_{1}+m_{2}\right)\left(m_{1}-m_{2}\right)}{m_{1}+m_{2}+\frac{I}{R^{2}}}} \)
(c) \( \sqrt{\frac{m_{1}+m_{2}+\frac{I}{R^{2}}}{m_{1}-m_{2}}} \)
(d) \( \sqrt{\frac{\frac{I}{R^{2}}}{m_{1}+m_{2}}} \)
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