Steel wire of length ‘L’ at 400C is suspended from the ceiling and then a mass ‘m’ is hung from its free end. The wire is cooled down from 400C to 300 Cto regain its original length ‘L’. The coefficient of linear thermal expansion of the steel is 10-5C-1. Young’s modulus of steel is 1011N/m2and 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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a
4 Kg
b
3 Kg
c
1 Kg
d
2 Kg
answer is B.
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Detailed Solution
as the length remain same then thermal stress is equal to longitudinal stress Yα∆t =mgπr2 m= Yα∆tπr2g =1011×10-5×10×π×10-610=3.14