# 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 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is Option 1) less than 3 Option 2) more than 3 but less than 6 Option 3) more than 6 but less than 9 Option 4) more than 9

As we learnt in

Analogue of second law of motion for pure rotation -

- wherein

Torque equation can be applied only about two points

(i) centre of motion.

(ii) point which has zero velocity/acceleration.

is zero at

t = 6 sec

No. of revolution  less than 6

Ans. 4

Option 1)

less than 3

This an incorrect option.

Option 2)

more than 3 but less than 6

This is the correct option.

Option 3)

more than 6 but less than 9

This an incorrect option.

Option 4)

more than 9

This an incorrect option.

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