Question

The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it ?
(a) The forces may be acting radially from a point on the axis.
(b) The forces may be acting on the axis of rotation.
(c) The forces may be acting parallel to the axis of rotation.
(d) The torque caused by some forces may be equal and opposite to that caused by other forces.

Answer 1

Explanation:

The relation for τ = F x r

here F is the force applied and r is the distance between force and axis of rotation . It is the cross product of F and r

Thus τ = F r sinθ

( a ) The force is acting from a point on the axis , therefore , there is no angle between F and r , means θ = 0 . It makes τ = 0

( b ) The force is acting on the  axis , therefore r = 0 . Thus τ = 0

( c ) When the force acts parallel to the axis , the torque can not be applied . Because the torque is due to tangential forces only .

( d ) When the forces applied cancel each other torques , even than the torque can be zero .

Thus all are compatible with the above statement .