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Question

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

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

## The correct option is C 30 Jω1=20 rad\sec, ω2=0, t = 4 sec. So angular retardation α=ω1−ω2t=204=5radsec2 Now angular speed after 2 sec ω2=ω1−αt=20−5×2=10radsec Work done by torque in 2 sec = loss in kinetic energy =12I(ω21−ω22)=12(0.20)((20)2−(10)2) =12×0.2×300=30J.

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