JEE Mains (Rotational Dynamics)

A pulley of radius 2 m is rotated about its axis by a force F =20t-5t² newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kgm², the number of rotations made by the pulley before its direction of motion it reversed, is

(a) more than 6 but less than 9

(b) more than 9

(c) less than 3

(d) more than 3 but less than 6