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Question

Steel wire of length 'L' at 40oC is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from 40oC to 30oC to regain its original length ′L′. The coefficient of linear thermal expansion of the steel is 10−5/oC, Young's modulus of steel is 1011N/m2 and radius of the wire is 1 mm. Assume that L>> diameter of the wire. Then the value of 'm' in kg is nearly

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Solution

The correct option is **A** 3

We know that

E=FA△LL⇒ΔLL=FAE......(i)

Also

ΔLL∝αΔT.....(ii)

from (i) and (ii)

FAE=αΔT

⇒mg=(αΔT)AE

⇒m=gαΔTAE

=10−5×10×π×10−6×101110

=π≈3

So correct answer is *a*

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