A pulley of radius \( 2 m \) is rotated about its axis by a force \( F=\left(20 t-5 t^{2}\right)...

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A pulley of radius \( 2 m \) is rotated about its axis by a force \( F=\left(20 t-5 t^{2}\right) \) newton (where \( t \) is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is \( 10 \mathrm{~kg} \mathrm{~m}^{2} \), the number of rotations made by the pulley before its direction of motion if reversed, is
[AIEEE 2011]
(a) Less than 3
(b) More than 3 but less than 6
(c) More than 6 but less than 9
(d) More than 9
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