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Two small balls A and B , each of mass m are joined rigidly by a light horizontal rod of length L . The rod is clamped at the centre in such a way that it can rotate freely about a vertical axis through its centre. The system is rotated with an angular speed $ω$ about axis. A particle P of mass m kept at rest sticks to the ball A as the ball collides with it. The new angular speed of the rod is $\frac{yω}{3}$ then the value of y .

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answer is 2.

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Detailed Solution

In this case there is no other force(torque) acting on the body, so the total angular momentum is conserved.

$Iw = I^{'} w^{'}$

$2 m (\frac{L^{2}}{4}) \times w = [(2 m) \frac{L^{2}}{4} + \frac{{mL}^{2}}{4}] w^{'} \Rightarrow w^{'} = \frac{2 w}{3}$

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