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

Question

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

Infinity Learn · Accepted Answer

as the length remain same then thermal stress is equal to longitudinal stress Yα∆t $$=mg$$$$π$$$$r2$$ $$m=$$ Yα∆t$$π$$$$r2g$$ $$=1011$$×$$10-5$$×$$10$$×π×$$10-610=3.14$$

Start JEE / NEET / Foundation preparation at rupees 99/day !!

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!