A simple pendulum having bob of mass m and length $l$ is pulled aside to make an angle $\mathrm{\theta }$ with the vertical. Find the magnitude of the torque of the weight of the bob about the point of suspension. At which position its torque is zero? At which $\mathrm{\theta }$ it is maximum?

Calculate the net torque on the system about the point $O$ as shown in figure if $F_1=11 \mathrm{N}, F_2=9 \mathrm{N},\mathit{ }{F}_3=10 \mathrm{N}, a=10 \mathrm{cm}$and$b=20 \mathrm{cm}.$(All the forces along the tangent).

Assuming frictionless contacts, determine the magnitude of external horizontal force $P$ applied at the lower end for equilibrium of the rod as shown in figure. The rod is uniform and its mass is $m\mathit{.}$

In the system as shown in figure, $\mathrm{AB}$ is a uniform rod of mass $10 \mathrm{kg}$ and $\mathrm{BC}$is a light string which is connected between wall and rod, in vertical plane. There is block of mass $15 \mathrm{kg}$ connected at $\mathrm{B}$with a light string. $[\text{Take }g=10 \mathrm{m} {\mathrm{s}}^{-2}]$ ($\mathrm{BC}$ and $\mathrm{BD}$are two different strings)

$\left(\mathrm{i}\right)$ Tension in the string $\mathrm{BC}$

$\left(\mathrm{ii}\right)$Hinge force exerted on beam at point $\mathrm{A}$

A rod of negligible mass having length $l=2 \mathrm{m}$is pivoted at its centre and two masses of $m_1=6 \mathrm{kg}$ and $m_2=3 \mathrm{kg}$ are hung from the ends as shown in figure.

$\left(\mathrm{a}\right)$Find the initial angular acceleration of the rod if it is horizontal initially.

$\left(\mathrm{b}\right)$ If the rod is uniform and has a mass of $m_3=3 \mathrm{kg}.$

$\left(\mathrm{i}\right)$ Find the initial angular acceleration of the rod.

$\left(\mathrm{ii}\right)$ Find the tension in the supports to the blocks of mass $3 \mathrm{kg}$ and $6 \mathrm{kg}$ $(g=10 {\mathrm{ms}}^{-2}).$

The uniform rod $AB$of mass m is released from rest when $\mathrm{\beta }= 60º.$ Assuming that the friction force between end $A$ and the surface is large enough to prevent sliding, determine (for the instant just after release)

$\left(\mathrm{a}\right)$The angular acceleration of the rod

$\left(\mathrm{b}\right)$ The normal reaction and the friction force at $A.$