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A ring of mass $M$  and radius R  is rotating with angular speed  $\omega$ about a fixed vertical axis passing through its centre  O with two point masses each of mass $\frac{M}{8}$  at rest at O . These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of the system is  $\frac{8}{9}\omega$ and one of the masses is at a distance of  $\frac{3}{5}R$ from  O. At This instant the distance of the other mass from  O is

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A uniform thin rod AB of mass M = 0.6 kg and length l = 60 cm stands at the edge of a frictionless table as shown in figure. A particle of mass m = 0.3 kg flying horizontally with velocity v₀ = 24 m/s strikes the rod at point P at a height h = 45 cm from the base and sticks to it. The rod is immediately driven off the table. If the time after collision when the rod becomes horizontal for the first time is found to be $=\frac{\mathrm{\pi }}{\ast \ast }\sec$, find the value of '**'(g = 10 m/s²).

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