The length og two metal wire is `l_(1)` when the tension in it is `F_(1)` and `l_(2)` when the tension is `F_(2)` .then the original length of the wire is

Explanation

Let I be the natural length of the wire. For the force` F_(1)` if elongation is `e_(1)`
`e_(1)=(F_(1)l)/(AY) rArr Y=(F_(1)l)/(Ae_(1))` Similarly for the force `F_(2)`, if elongation is `e_(2)`
`e_(2)=(F_(2)l)/(AY)= rArr Y=(F_(2)l)/(Ae_(2)), l_(2)=l+e_(1) and l_(2)=l+e_(2)`
`Y=(F_(1)l)/(A(l_(1)-l))=(F_(2)l)/(A(l_(2)-l))= F_(1)(l_(1)-l)=F_(2)(l_(1)-l) and F_(1)l_(2)-F_(1)=F_(2)l_(1)-F_(2)l`
`(F_(2)-F_(1))=l=l_(1)F_(2)-l_(2)F_(1) or l=(l_(1)F_(2)-l_(2)F_(1))/((F_(2)-F_(1)))`