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11. A rod $OA$ of mass ' $m$ ' and length $L$ hinged at end $O$ can rotate smoothly in vertical plane about horizontal axis passing through $\mathrm{O}$. It is released from a horizontal position as shown in the figure and strikes a block of mass M kept vertically below $\mathrm{O}$ at distance $\mathrm{L}$ on a smooth horizontal surface. The block after collision moves on the smooth vertical circular track of diameter $L$ such that the force exerted by the circular track on the block at point $C$ is on third of its weight. If the rod after collision rotates through an angle $30^{\circ }$ from the horizontal, fin the ratio of masses $\mathrm{M}/\mathrm{m}$. 12. A plank of mass $\mathrm{M}$ is placed over smooth triangular wedge with angle of inclination $30^{\circ }$. Block of mass $m$ is connected to the plank by massless string. A cylinder of mass $M$ and radius $R$ is

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Updated on: Feb 7, 2023