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Question

A body starts rotating from rest under the influence of a variable torque τ=10 cos2θ where, τ is in J. Find the total work done by the torque to rotate the body from 0 to 180.

A
Zero
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B
5π J
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C
900 J
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D
10π J
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Solution

The correct option is B 5π J
Given, τ=10cos2θ
Since we know that,
Work done by variable torque
W=τdθ
Now, work done to rotate the body from 0 to 180 i.e π rad is given by
W=π010cos2θ dθ
W=10π0cos2θ dθ
W=10π0(cos2θ+1)2dθ (ascos2θ=cos2θ+12)
W=5π0(cos2θ+1)dθ
W=5([sin2θ2]π0+[θ]π0)
W=5(0+π)=5π J
So, option B is correct.

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