Introduction:
In physics, equilibrium refers to a state in which the net force and net torque acting on a system are both zero. When the net force is zero, the system is in translational equilibrium, and when the net torque is zero, the system is in rotational equilibrium. In this question, we are specifically addressing the condition for rotational equilibrium and the point about which torques are taken.

Explanation:
To understand why the correct answer is option 'C' (the center of mass of the system), let's first define what torque is. Torque is the measure of the force's tendency to cause an object to rotate about an axis or pivot point. It is given by the product of the force applied and the perpendicular distance from the axis of rotation to the line of action of the force.

The Center of Mass:
The center of mass of a system is the point at which the entire mass of the system can be considered to be concentrated. It is a mathematical concept that simplifies the analysis of systems by allowing us to treat the entire system as if all the mass were located at a single point.

Equilibrium and Torques:
For a system to be in equilibrium, the net torque acting on it must be zero. This means that the clockwise torques must balance the counterclockwise torques. If the torques are taken about any other point in the system (option 'A'), the torques may not balance each other, and the system will not be in equilibrium.

Equilibrium and Center of Mass:
However, when the torques are taken about the center of mass of the system, the system will be in equilibrium. This is because the center of mass is a special point in the system where the distribution of mass is balanced. When torques are taken about the center of mass, the clockwise torques will exactly balance the counterclockwise torques, resulting in a net torque of zero.

Example:
For example, if we consider a uniform rod pivoted at one end, the center of mass of the rod will be located at its midpoint. If we apply a force perpendicular to the rod at any other point, the torques will not balance each other, and the rod will rotate. However, if we apply the force at the center of mass of the rod, the torques will balance, and the rod will remain in rotational equilibrium.

Conclusion:
In conclusion, for a system to be in equilibrium, the net torques acting on it must balance. This is achieved by taking the torques about the center of mass of the system. Taking torques about any other point in the system will not result in equilibrium.