A metallic wire is suspended by suspending weight to it. If S is longitudinal strain and Y its young's modulus of elasticity then potential energy per unit volume will be

Options

A. `Y alpha^(2)`
B. `(1)/(2) Y alpha^(2)`
C. `(3)/(2) Y alpha^(2)`
D. `(Y)/(alpha^(2))`

Answer

B

Explanation

Elastic potential energy per unit volume is `u= (1)/(2) xx` stress `xx` strain `= (1)/(2) xx (Y xx "strain") xx` strain
Here, strain `= alpha`
`:. u= (1)/(2) xx (Y xx alpha) xx alpha = (1)/(2) Y alpha^(2)`