Torques on a balance beam

A light beam rests on a pivot. A mass M is hung a distance r from the pivot on the right end of the beam, and a mass m is hung a distance R from the pivot on the left end of the beam, as shown. The beam is balanced. 

(a) Draw a free-body diagram for the beam, and find an expression for the magnitude of all of the forces on the beam.

(b) Find the magnitude and direction of the torque about the pivot point on the beam due to each of the forces on it.

(c) How must the distances R and r be related in order that the beam is balanced?

(d) Find the magnitude and direction of the torque about the right end of the beam due to each of the forces acting on it. What is the net torque on the beam around this point? 

(e) What is the net torque on the beam around a point a distance x from the left end of the beam, as shown?