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  4. A smooth ring P of mass m can slide on a fixed horizontal rod. A string tied to the ring passes over a fixed pulley and carries a block Q of mass (m / 2) as shown in the figure. At an instant, the string between the ring and the pulley makes an angle 60° with the rod. The initial acceleration of the ring is

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Q. A smooth ring $P$ of mass $m$ can slide on a fixed horizontal rod. A string tied to the ring passes over a fixed pulley and carries a block $Q$ of mass $(m / 2)$ as shown in the figure. At an instant, the string between the ring and the pulley makes an angle $60^{\circ}$ with the rod. The initial acceleration of the ring isPhysics Question Image

Laws of Motion

Solution:

$\frac{m}{2} g -T=\frac{m}{2} a....$(i)
$T \cos 60^{\circ}=\frac{ ma }{\cos 60^{\circ}} ....$(ii)
Solving (i) and (ii)
acceleration of ring $=\frac{2 g }{9}$