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Question

A pulley wheel of diameter 2 cm has a 1 m long cord strapped across its periphery. The wheel is initially at rest. If it is given an angular acceleration of 0.1 rad/s2, then the time taken for the cord to unwind completely is

A
20 s
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B
203 s
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C
205 s
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D
1010 s
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Solution

The correct option is C 205 s
Initial angular velocity (ω0)=0 rad/s
Given, angular acceleration (α)=0.1 rad/s2

Total angular displacement of the pulley wheel
θ=lr=1001=100 rad

Since. angular acceleration is uniform, we are free to use equation of motion.
θ=w0t+12αt2
100=0+12×(0.1)t2
100=120t2
t2=2000
t205 s

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