Question

What force is responsible for net torque on the pulley?

Answer 1

Hint: The tension forces on the rope that goes around the body of the pulley plays an important role in rotating the pulley around its hinged point.
Where the tension force of the rope is the pulling force that acts along the whole rope, caused due to stretching or by the suspension of some load on the rope.

Complete answer:
The net torque on a pulley is determined by the tension forces of the rope or the string that moves around the pulley.
The tension force and the friction between the rope and the pulley causes the pulley to rotate around the hinge.
The figure shows two tension forces around the pulley

The net force or the resultant tension force around the pulley wheel determine the direction of torque and the direction of the rotation of the pulley.
The net moment generated and the direction of moment can be determined by:
\[\overrightarrow M = \overrightarrow r \times \left( {\overrightarrow {{T_1}} - \overrightarrow {{T_2}} } \right)\]
Where \[\overrightarrow r \] is the radius vector of the pulley. The direction of the moment \[\overrightarrow M \]
 vector gives us the direction of torque and the \[\overrightarrow M \] vector gives us the actual value of torque.

Note:
The tension force merely acts as an action force, but the real torque generated on the pulley is due to the friction between the rope and the pulley surface. The friction opposes the rope in the backward direction whereas the friction on the pulley surface causes the pulley to rotate in the direction of rotation. In order to get the value of the moment generated we use the cross product of the vector by placing the radius vector first. If we interchanged the places of tension and radius the direction changes thus we land up with the wrong answer.