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A rod of length $R$ and mass $M$ is free to rotate about a horizontal axis passing through hinge $P$ as shown in the figure. First it is taken aside such that it becomes horizontal and then released. At the lowest point the rod hits the block $B$ of mass m and stops. If mass of rod is $\sqrt{60} k g,$ find mass of the block if it just complete the circle.

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answer is 2.

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Detailed Solution

$\frac{M g r}{2} = \frac{1}{2} \frac{M r^{2}}{3} ω^{2}$

$ω = \sqrt{\frac{3 g}{r}}$

$\sqrt{5 g r} m \times r = \frac{M r^{2}}{3} \times \sqrt{\frac{3 g}{r}}$

$m = 2 k g$

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