If M and m are particles connected by light inextensible string. M is held at center and
Rotated about horizontal axis as M is in equilibrium.What is torque ABOUT ITS CENTER

Hint - remember that torque about the center of M is equal to the applied force times the perpendicular distance of the forec vector to the center of M. So you need to consider: what force is being applied here, and at what distance from the center of M?