A slender uniform rod of mass $M$ and length $l$ is pivoted at one end, so that it can rotate in a vertical plane (see the figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\mathrm{\theta }$ with the vertical is,

In the given figure, the bar is uniform and weighing $500 \mathrm{N}$. How large must $W$ be if $T_1$ and $T_2$ are to be equal?

Find force $F$ required to keep the system in equilibrium. The dimensions of the system are $d=0.3 \mathrm{m}$ and $a=0.2\mathrm{m}$. Assume the rods to be massless.

An equilateral prism of mass $m$ rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force $F$ is applied on the prism as shown in the figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is,

Each pulley in figure has radius r and moment of inertia $I$. The acceleration of the block is

In the pulley system shown, if the radii of the bigger and smaller pulleys are $2 \mathrm{m}$ and $1 \mathrm{m}$, respectively, and the acceleration of block $\mathrm{A}$ is $5 \mathrm{m} {\mathrm{s}}^{-2}$ in the downward direction, then the acceleration of block $\mathrm{B}$ will be:

A uniform rod of mass $15\mathrm{}\mathrm{k}\mathrm{g}$ is held stationary with the help of a light string as shown in figure. The tension in the string is