Question

Obtain an expression for strain energy in a strained wire.

Answer 1

we know, Young's modulus is the ratio of stress to strain. e.g., Y = stress/strain.
if we assume a wire of length L, area of cross section A is fixed at one end and stretched by suspended a load M from the other end due to this extension of wire is x.

so, Young's modulus of wire , Y = FL/Ax
or, F = YAx/L
we know, workdone , W = F.dx
so, W = (YAx/L)dx
or, W = 1/2 × YAx²/L
W = 1/2 × {YAx/L} × x
W = 1/2 × F × x

hence, Work done = 1/2 × load × extension

now, potential energy = workdone by external applied force
= 1/2 × load × extension.