A uniform metal rod of `2mm^(2)` area of cross section is heated from `0^(@)C` to `20^(@)C`. The coefficient of linear expansion of the rod is `12xx10^(-6)//""^(@)C`. Its Young's modulus of elasticity is `10^(11)N//m^(2)`, then the energy stored per unit volume of rod is,

Options

A. `1440 J//m^(3)`
B. `2880 J//m^(3)`
C. `1200 J//m^(3)`
D. `3880J//m^(3)`

Answer

B

Explanation

`u=(1)/(2)(F)/(A) xx (l)/(L) =(1)/(2)(F)/(A) xx prop Delta t`
But `Y=(F)/(A) (l)/(L) " " therefore F=(Yal)/(L)`
`u=(1)/(2)Y(alpha Delta t)^(2)`