Correct Answer - `U=(F^(2)l)/(6AY)`

As discussed Mechanics the tension `T` in the string at a distance `x` from its free end is given

`T=F/lx`

Hence stress, `p=T/A=F/(Al)x`

Substituting `p` in the formula`U=1/(2Y)intp^(2)dV`

we have `U=1/(2Y)int_(0)^(l) (F^(2))/(A^(2)l^(2))x^(2)dV`, where d`V=Adx`

This gives `U=(F^(2)l)/(6AY)`