A matallic wire is stretched by suspending weight to it. If `alpha` is the longitudinal strain and Y its Young's modulus of elasticity, shown that the elastic potential energy per unit volume is given by `Y alpha^(2)//2`

Explanation

Stress =Young's modulus `xx `strain = Y `xxalpha`
Elastic potential energy per unit volume is ,
`u = 1/2 xx stress xx strai n = 1/2 xx Y alpha xx alpha`
`1/2 Y alpha^(2)`.