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Question

A pulley wheel of diameter 10 cm has a 1 m long cord wrapped around its periphery. The wheel is initially at rest. Assuming angular acceleration of wheel to be uniform and the time taken for the cord to unwind completely to be 18 s, find its tangential acceleration.

A
6.17 mm/s2
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B
2 mm/s2
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C
0.1 mm/s2
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D
0.01 mm/s2
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Solution

The correct option is A 6.17 mm/s2
Given,
Initial angular velocity (ωo)=0 rad/s
Time taken to unwind completely (t)=18 s

Length of cord wound on pulley =1 m

Angle of windings, (θ)=lr=10.05=20 rad

Since angular acceleration is uniform, from the equation
θ=ω0t+12αt2θ=12αt2
(ω0=0)
α=2θt2=2×20(18)2 rad/s2
Tangential acceleration at=rα
at=0.05×2×20(18)2 m/s2
at=6.17×103 m/s2
at=6.17 mm/s2

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