The length of a steel wire is `l_(1)` when the stretching force is `T_(1)` and `l_(2)` when the stretching force is `T_(2)`. The natural length of the wire is

Explanation

Let l and A be the original length and area of cross-section of the metal wire.
Change in length in the first case = `(l_(1)-l)`
Change in length in the second case` = (l_(2)-l)`
`:. Y=(T_1)/(A) xx (l)/(l_(1)-l) = (T_2)/(A) xx (l)/(l_(2)-l)`
or `T_(1)l_(2)-T_(1) l=T_(2) l_(1)-T_(2)l`
or `l(T_(2)-T_(1)) = T_(2) l_(1)-T_(1)l_(2)`
or `l=(T_(2)l_(1)-T_(1)l_(2))/(T_(2)-T_(1))`.