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Question

A cord is wound around the circumference of a bicycle wheel (without tyre) of diameter 1 m. A mass of 2 kg is tied to the end of the cord and it s allowed to fall from rest. The weight falls 2 m in 4 s. The axle of the wheel is horizontal and the wheel rotates with its plane vertical. The angular acceleration produced is (Take g=10 ms2)

A
0.5 rad s2
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B
1.0 rad s2
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C
2.0 rad s2
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D
4.0 rad s2
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Solution

The correct option is A 0.5 rad s2

We first find the acceleration a by using the relation
s=ut+12at2
or 2=0+12×a×(4)2
which gives a=14 ms2. Now R=0.5 m.

We know that the relation between linear acceleration (a) and angular acceleration (α) for pure rolling is
α=aR=14×0.5=12=0.5 rad s2

Hence the correct choice is (a).

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