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. `0.5"Y X"^(2)`
B. `0.5"Y"^(2)"X"`
C. `2" Y X"^(2)`
D. `"Y X"^(2)`

Answer

A

Explanation

As, `U=(1)/(2)xx" stress "xx" strain"`
Also, `Y=("Stress")/("Strain")`
or Stress `=Y xx" strain "=Y xx X`
`:.U=(1)/(2)xx(YX)(X)" or "U=(1)/(2)YX^(2)`
or `" "U=0.5" YX"^(2)`