A 0.74-m diameter solid sphere can be rotated about an axis through its center by a torque of 10.8 m*N which accelerates it uniformly from rest through a total of 160 revolutions in 14.0 s.
1. What is the mass of the sphere?

Mass of the sphere is 19.2 kg

Explanation:

We have given diameter of the sphere d = 0.74 m

So radius r = 0.37 m

Initial angular velocity

Time t = 14 sec

Angular displacement

From second equation of motion

So

Torque is given

Torque is equal to , here I is moment of inertia and angular acceleration

So

Moment of inertia of sphere is equal to

So

M = 19.23 kg

So mass of the sphere is 19.23 kg