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Question

# A wheel is rotating with an angular speed 20rad/s. It is stopped to rest by applying constant torque in 4s. If the moment of inertia of the wheel about is axis is 0.20kg/m2, then the work done by the torque in two seconds will be :

A
10J
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B
20J
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C
30J
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D
40J
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Solution

## The correct option is C 30Jω1=20rad/s,ω=0,t=4s. So angular retardationα=ω1−ω2t=204=5rad/s2Now, angular speed after 2sω2=ω1−αt=10rad/swork done by torque in 2s = loss in kinetic energy=12I(ω21−ω22)=12(0.20)[(20)2−(10)2]=12×60=30

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