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Question

A cord is wound a round the circumfererence of a wheel of mass 50Kg and diameter 0.3m. The axis of the wheel is horizonatal. A mass of 0.5Kg is attached at the end of the cord. Find the angular acceleration of the wheel?


A

1.1rad/s2

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B

1.2rad/s2

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C

1.3rad/s2

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D

1.4rad/s2

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Solution

The correct option is C

1.3rad/s2


Here the weight of the 0.5Kg applies a torque on the wheel about its axis.
τ=rFsinθ
Moment of Inertia I=MR22Butτ=Iαα=τI=rFsinθ×2MR2Here r=R=0.15mF=mg=(0.5×9.8)Nθ=90M=50KgSubstituting,α=0.15×0.5×9.8×sin90×250×0.15×0.15=1.3rad/s2


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