When a force is applied at one end of an elastic wire, it produce a strain E in the wire. If Y is the Young's modulus of the material of the wire, the amount of energy stored per unit volume of the wire is given by

Options

A. `YxxE`
B. `(1)/(2)(YxxE)`
C. `YxxE^(2)`
D. `(1)/(2)(YxxE^(2))`

Answer

D

Explanation

(d) Energy per unit volume `=(1)/(2)xx"Stress"xx"strain"`
`=(1)/(2)xx(Yxx"strain")xx"strain"=(1)/(2)xxYxxE^(2)`