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A smooth ring \( A \) mass \( m \) can slide on a fixed horizontal rod. A string tied to the ring passes over a fixed pulley \( B \) and carries a block \( C \) of mass \( M(=2 m) \) as shown in figure-2.198. At an
\( \mathrm{P} \) instant the string between the ring and the pulley makes an W angle \( \alpha \) with the rod. (a) Show that, if the ring slides with a speed \( v \), the block descends with speed \( v \cos \alpha \); (b) With what acceleration will the ring start moving if the system is released from rest with \( \alpha=30^{\circ} \).
Figure 2.198
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