A wire of length L and cross sectional area A is made of a material of Young's modulus Y. If the wire is streched by an amount x, the work done is………………

Explanation

Let during the stretching of the wire, its extension at an instant of tme is `x` and it is further stretched by `dx`. The restoring force acting at that instant is
`Y=(F//A)/(x//L)impliesF=(Yx)/(1xxL)xxA`

The small amount of work done during the stretching by `dx` by the applied force
`dW=Fdx=(YxA)/L dx`
Total work done for stretching for distance `x` can be by integrating above equation.
`W=int_(0)^(x)(YxAdx)/L=(YA)/Lint_(0)^(x) xdx=(YAx^(2))/(2L)`