A body starts rotating from rest under the influence of a variable torque τ=10cos2θ 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
5πJ
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C
900J
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D
10πJ
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Solution
The correct option is B5πJ 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 πrad is given by W=∫π010cos2θdθ ⇒W=10∫π0cos2θdθ ⇒W=10∫π0(cos2θ+1)2dθ(ascos2θ=cos2θ+12) ⇒W=5∫π0(cos2θ+1)dθ ⇒W=5([sin2θ2]π0+[θ]π0) ⇒W=5(0+π)=5πJ
So, option B is correct.