A pulley of radius 2m is rotated about its axis by a force F=20t-5t2 newton [where t is measured in second) applied tangentially. If the moment of Inertia of the pulley about its axis of rotation is 10kg- m2.The number of rotations made by the pulley before its direction of motion reversed is

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More than 3 but less than 6

More than 9

More than 6 but less than 9

less than 3

answer is A.

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Detailed Solution

F=20t−5t2 ⇒α=FRI=(20t−5t2)210=4t−t2 ⇒dωdt=4t−t2 ⇒∫ ω0dω=∫0t(4t−t2) dt ⇒ω=4t22−t33=2t2−t33 ∴[ω=0 at t=0 or 6s] ⇒∫ θ0dθ=∫06 (2t2−t33)dt ⇒θ−0=(2t33−t43×4)60 ⇒θ=36rad ⇒n=362π<6

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