4 A uniform solid sphere, of mass 14 kg and radius 0.25 m , is rotating about a fixed axis which is a diameter of the sphere. A couple of constant moment 4.2 Nm about the axis, acting in the direction of rotation, is applied to the sphere.

1. Find the angular acceleration of the sphere. During a time interval of 30 seconds the sphere rotates through 7500 radians.
2. Find the angular speed of the sphere at the start of the time interval.
3. Find the angular speed of the sphere at the end of the time interval.
4. Find the work done by the couple during the time interval.