If in a wire of Young's moduls `Y`, longitudinal strain `X` is produced then the potential energy stored in its unit volume will be:

Options

A. `xy^2`
B. `2xy^2`
C. `(1)/(2)y^2x`
D. `(1)/(2)yx^2`

Answer

D

Explanation

Energy stored per unit volume `=(1)/(2)xx`stress`xx`strain
From the difinition of Young's modulus of wire
`Y=(stress)/(strai n)`
`impliesstress=Yxxstrai n`
Given, strain`=X`
Therefore, `U=(1)/(2)XX`Young's modulus `xx(strai n)^2`
`=(1)/(2)xxYxx x^2`