A thin rod of negligible mass and a cross-section of `2 xx 10^(-6) m^(2)` suspended vertically from one end, has a length of `0.5 m` at `200^(@)C`. The rod is cooled at `0^(@)C`, but prevented from contracting by attaching a mass at the lower end. The value of this mass is : (Young's modulus `=10^(11) N//m^(2)`, Coefficient of linear expansion `10^(-5) K^(-1) and g = 10 m//s^(2)`):

Options

A. `20 kg`
B. `30 kg`
C. `40 kg`
D. `50 kg`

Answer

C

Explanation

Strain `(epsilon) = (Delta l)/(l) = prop DeltaT = (10^(-5))(200) = 2 xx 10^(-3)`
Stress `= Y("strain")`
Stress = `10^(11) xx 2xx10^(-3)=2xx10^(8)N//m^(2)`
`rArr` Required force = stress `xx` Area
`=(2xx10^(8))(2xx10^(-6)) = 4 xx 10^(2) = 400N`
`:.` Mass to be attached = `(400)/(g) = 40 kg`.