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Question

A pulley of radius 2 m is rotated about its axis by a force F=(20t5r2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis fo rotation is 10 kgm2, the number of rotations made by the pulley before its direction of motion is reversed, is:

A
less than 3
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B
more than 3 but less than 6
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C
more than 6 but less than 9
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D
more than 9
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Solution

The correct option is B more than 3 but less than 6
τ=(20t5t2)2=40t10t2
α=τI=40t10t210=4tt2
ω=t0αdt=2t2t33
When direction is reversed, ω is zero. So
2t2t33=0t3=6t2t=6s
θ=ωdt=60(2t2t33)dt=[2t33t412]60=36 rad
Number of revolution = 362π = Less than 6

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