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Question

Steel wire of length L at 40C is suspended from the ceiling and then a mass m is hung from its free end. The wire is cooled down from 40C to 30C to regain its original length L. The coefficient of linear thermal expansion of the steel is 105/C. Young's modulus of steel is 1011N/m2 and radius of the wire 1 mm. Assume that L>> diameter of the wire. Then the value of m in kg is nearly.

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Solution

Y=stressstrain=mg/ΔΔl/l

Y=mglAΔl

Y=mglAlΔT=mgAΔT

m=YAΔTg

=104×π(103)2×103×1010

n3

m=3

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