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Question

A bucket is being lowered down into a wall through a rope passing over a fixed pulley f radius 10 cm. Assume that the rope does not slip on the pulley. Find the angular acceleration of the pulley at an instant when the bucket is going down at a speed of 20 cm/s and has a acceleration of 4ms−2.

A
10 rad s2
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B
20 rad s2
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C
30 rad s2
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D
40 rad s2
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Solution

The correct option is D 40 rad s2
Since there is no slipping, the linear acceleration of rope going down would be equal to the tangential acceleration of rotation of pulley at all points.
Hence, a=Rα
α=aR=40rad/s

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