for an object in equillibrium the net torque acting on it vanishes only if each torque is calculated about?

the same point.

Torque must be zero about any axis, in equilibrium

In order for the net torque acting on an object in equilibrium to vanish, each torque must be calculated about the same point, known as the axis of rotation. This point can be chosen freely, as long as all torques are based on the same reference point.

To determine the axis of rotation, you can follow these steps:

1. Identify the object and its various forces acting on it.
2. Determine the individual torque produced by each force.
3. Choose a reference point or axis of rotation about which to calculate the torques.
4. Calculate the torque produced by each force based on the chosen reference point.
5. Sum up all the torques about the reference point.
6. If the net torque (the sum of all torques) around the chosen reference point is zero, then the object is in rotational equilibrium. If the net torque is nonzero, the object will experience rotational motion.

Remember that torque is defined as the product of the force and the perpendicular distance from the axis of rotation to the line of action of the force. By considering all the torques around the same axis of rotation, you can determine if an object is in rotational equilibrium or if it will experience rotational motion.