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 its original length be l
we know `e prop T rArr (l_1 - l) prop T_1 ` …..(1)
`(l_2 - l)prop T_2 ` …….(2)
From (1) and (2) `(l_1-l)/(l_2 - l) = T_1/T_2 rArr T_2 l_1 - T_2 l = T_1 l_2 - T_2 l`
` T_2l_1 - T_1l_2 = (T_2 - T_1)l rArr l = (T_2l_1 - T_1l_2)/(T_2 - T_1)`