proportional to θ , equal to τθ. Where τ is the restoring couple per unit angle of twist. τ can be measured independently e.g. by applying a known torque and measuring the angle of twist.
The gravitational force between the spherical balls is the same as if their masses are concentrated at their centres. Thus if d is the separation between the centres of the big and its neighbouring small ball, M and m their masses, the gravitational force between the big sphere and its neighouring small ball is. Mm G d ( . ) If L is the length of the bar AB , then the torque arising out of F is F multiplied by L.
At equilibrium, this is equal to the restoring torque and hence Mm L τ θ ( . )