Steel wire of length 'L' at `40^@C` is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from `40^@C to 30^@C` to regain its original length 'L'. The coefficient of linear thermal expansion of the steel is `10^-5//^@C`, Young's modulus of steel is `10^11 N//m^2` and radius of the wire is 1mm. Assume that `L gt gt` diameter of the wire. Then the value of 'm' in kg is nearly

Answer

3

Explanation

`(F)/(A)=Y(DeltaL)/(L)rArr(mg)/(A)=Y(alphaDeltatheta)`
`m=(AYalpha(Deltatheta))/(g)=(pir^(2)yalpha(Deltatheta))/(g)=(pi(10^(-3))^(2)xx10^(11)xx10^(-5)xx10)/(10)=pi~~3kg`.