Question

A large, solid sphere (mass = 103 kg) with a radius of 19 cm is suspended by a vertical wire. In order to rotate the sphere about the wire by an angle of 0.75 radians and hold it in that orientation, a torque of 0.16 Nm is needed. What is the period of oscillation of the rotating system once the sphere is released? Your answer should be in s, but enter only the numerical part in the box.

Answer 1

Torque acting on the sphere is

which keeps it on hold at an angle of

So, the torsional constant is

Mass of the pendulum bob is

and it has a radius of

So, moment of inertia of the pendulum sphere is

So, period of oscillation of the system is hence given by the expression