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Question

A pulley of 10 cm diameter is wrapped with a cord of length 2 m around its periphery. If pulley is initially at rest and is given an angular acceleration of 0.5 rad/s2, then total angular displacement of the pulley for the cord to unwind completely and the time taken by the cord to unwind completely are

A
20 rad,10 s
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B
20 rad,410 s
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C
40 rad,10 s
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D
40 rad,410 s
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Solution

The correct option is D 40 rad,410 s
Initial angular velocity (ω0)=0 rad/s
Angular acceleration (α)=0.5 rad/s2

Total angular displacement for the cord to unwind completely θ=lr=2005=40 rad
Since the angular acceleration is uniform, we can use
θ=ω0t+12αt2
40=12×0.5t2 (ω0=0)
t2=160
t=410s

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