91Ó°ÊÓ

Torque is defined as the measure of the force that causes an object to rotate about an axis. It is also called the rotational equivalent of linear force.

Mathematically, torque is represented as follows:

\(\begin{align}\vec \tau &= \vec r \times \vec F\\\left| \tau \right| &= rF\sin \theta \end{align}\) … (i)

Here, F is the applied force, and r is the perpendicular distance between the point about which the torque is calculated and the point of application of force.

There is a torque due to the force of gravity (weight) on the left block that will accelerate the rod anti-clockwise. Similarly, there will be a clockwise torque due to the weight of the right block.

Suppose the clockwise direction is positive. The net torque acting on the system will be given as follows:

\(\begin{align}\sum \tau &= mg{l_2} + \left( { - mg{l_1}} \right)\\ &= mg{l_2} - mg{l_1}\\ &= mg\left( {{l_2} - {l_1}} \right)\end{align}\)

Thus, the net torque is \(mg\left( {{l_2} - {l_1}} \right)\) in the clockwise direction.