A metallic wire is stretched by suspending weight from it if `alpha` is the longitudinal strain & y is the young's modulus, show that elastic potential energy per unit volume is given by `(1)/(2)yalpha^(2)`.

Options

A. `Yalpha^(2)`
B. `(1)/(2)Yalpha^(2)`
C. `(3)/(2)Yalpha^(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(Yxx"strain")xx"strain"`
Here, `"strain"=alpha`
`thereforeU=(1)/(2)xx(Yxxalpha)xxalpha`
`=(1)/(2)Yalpha^(2)`