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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 0.20kgm2, 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 J
ω1=20 rad\sec, ω2=0, t = 4 sec. So angular retardation α=ω1ω2t=204=5radsec2
Now angular speed after 2 sec ω2=ω1αt=205×2=10radsec
Work done by torque in 2 sec = loss in kinetic energy =12I(ω21ω22)=12(0.20)((20)2(10)2)
=12×0.2×300=30J.

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