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A wire of length L and cross-sectional a...

A wire of length L and cross-sectional area A is made of a material of Young's modulus Y. IF the wire is stretched by an amount x, the workdone is

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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)`
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