A wire of length L and area of cross section A is made of a material of Young's modulus Y. If it is stretched by an amount x, the work done is given by

Explanation

Restoring force in extension x = F =`(AY x)/(L)`
Work done in stretching it by dx = dw = F.dx
Work done in stretching it from zero to x = W = `int dw = int_(0)^(x)Fdx`
`W = int_(0)^(x)(AY )/(L)dx=(1)/(2)(AY x^(2))/(L)`