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

Options

A. 2880 `j//m^(3)`
B. `1500 J//m^(3)`
C. `5760 J//m^(3)`
D. `1440 J//m^(3)`

Answer

A

Explanation

Energy stored per unit volume
`=(1)/(2) ("stress" xx "strain") = (1)/(2) Y ( "strain ")^(2) = (1)/(2) Y (alpha Delta theta)^(2) = (1)/(2) xx 10^(11) xx (12xx10^(-4)xx 20)^(2) = 2880 J//m^(3)`