Define strain energy and derive the equa-
tion for the same.

Explanation

Starin energy : The energy developed in
(string) a body when it is strained is called
strain energy.
Let a force F be applied on lower end of
wire, fixed at the upper end. Let the
extension be dl.
`therefore"work done"=dW=dl`
Total work done in stretching it from 0
to`l=W=int_(0)^(l)dW=int_(0)^(l)Fdl`
`thereforeW=int_(0)^(l)(Yal)/(L)=(Yal^(2))/(2L)=(1)/(2)(Yal.)/(L).l`
`[becauseF=(Yal)/(L)]`
`W=(1)/(2)xx"stretching force"xx"elongation"`
`therefore`Work done per unit volume
`=(1)/(2)xx("stretching force"xx"elongation")/(aL)`
`=(1)/(2)xx"stress"xx"strain"`