A uniform rod of mass $m=2\sqrt{10}\mathrm{k}\mathrm{g}$ and length $l$ can rotate in vertical plane about a smooth horizontal axis hinged at point $H$. It is released from initial position making an angle of ${37}^{\mathrm{o}}$ with horizontal. Find force (in $\mathrm{N}$) exerted by the hinge just after the rod is released from rest.

A mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

A thin circular coin of mass $5 \mathrm{gm}$ and radius $\frac{4}{3} \mathrm{cm}$ is initially in a horizontal $xy$-plane. The coin is tossed vertically up ($+z$ direction) by applying an impulse of $\sqrt{\frac{\mathrm{\pi }}{2}}\times {10}^{-2} \mathrm{N}-\mathrm{s}$ at a distance $\frac{2}{3} \mathrm{cm}$ from its center. The coin spins about its diameter and moves along the $+z$ direction. By the time the coin reaches back to its initial position, it completes $n$ rotations. The value of $n$ is _____.

[Given: The acceleration due to gravity $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

An annular disk of mass $M$, inner radius $a$ and outer radius $b$ is placed on a horizontal surface with coefficient of friction $\mu$, as shown in the figure. At some time, an impulse $J_0\stackrel{\wedge }{x}$ is applied at a height $h$ above the center of the disk. If $h=h_m$ then the disk rolls without slipping along the $x$-axis. Which of the following statement(s) is(are) correct?

One end of a uniform rod of length l and mass is hinged at A. it is released from rest from horizontal position AB as shown in figure, The force exerted by the rod on the hinge when its becomes vertical is

A time varying force $F=2t$ is applied on a spool as shown in diagram. The angular momentum of the spool at time t about bottommost point is

A Uniform rod $AB$ is hinged at its end $A$ and the other end of the rod is connected to a block through a massless string as shown in the figure. The pulley is smooth and massless. Masses of the block and the rod are same and are equal to $m$. The acceleration of the block just after the release from this position is