Torque and Equilibrium:
- Torque is the rotational equivalent of force. It is the measure of the tendency of a force to rotate an object about an axis.
- When multiple torques act on a system, the net torque determines the rotational state of the system.
- If the net torque is zero, the system is in rotational equilibrium, meaning it is not rotating.
- The condition for rotational equilibrium is that the sum of the clockwise torques must be equal to the sum of the counterclockwise torques.

Choosing the Point of Calculation:
- To determine whether a system is in equilibrium, we need to calculate the net torque.
- The point about which the torques are calculated is crucial for obtaining accurate results.
- The torque exerted by a force depends on the distance between the point of calculation and the line of action of the force.
- The perpendicular distance between the point and the line of action is called the lever arm.
- The torque exerted by a force is given by the formula: Torque = Force × Lever arm.

Option A: Any Point on the System:
- The statement that the net torques must balance when taken about any point on the system is correct.
- This is because the net torque calculation is independent of the choice of the point of calculation.
- When calculating the net torque, we consider all the forces acting on the system and their respective lever arms.
- As long as we include all the forces and their lever arms, the net torque will be the same regardless of the point of calculation.
- This means that the rotational equilibrium condition holds regardless of the reference point chosen.
- Therefore, option A is the correct answer.

Option B: The Centre of the System:
- The statement that the net torques must balance only when taken about the center of the system is incorrect.
- While it is true that taking torques about the center of mass simplifies calculations, it is not a requirement for equilibrium.
- Equilibrium can be determined by calculating torques about any point on the system.
- The net torque will still be zero if the sum of the clockwise torques is equal to the sum of the counterclockwise torques, regardless of the point of calculation.

Option C: The Centre of Mass of the System:
- The statement that the net torques must balance only when taken about the center of mass of the system is incorrect.
- Similar to option B, taking torques about the center of mass is not a requirement for equilibrium.
- However, considering the center of mass can simplify calculations as it allows for the reduction of the number of forces and lever arms to be considered.
- But it is important to note that equilibrium can still be determined by calculating torques about any point on the system.

Option D: None of These:
- The statement that none of the above options are correct is incorrect.
- As explained, option A is the correct answer.
- The net torques must balance when taken about any point on the system for the system to be in equilibrium.
- This is a fundamental principle in rotational mechanics.