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 .`l`. be the original length and `l_(3)` be the length of the wire when the tension is 9N. We know `e propF`
`rArr (l_(1)-l) prop 4 ……. (1), (l_(2)-l) prop 5…….. (2)`
`(l_(3)-l) prop 9…….. (3)`
From (1) & (2) `(l_(1)-l)/(l_(2)-l) =(4)/(5) rArr 5l_(1) -5l=4l_(2)-4l`
`l=5l_(1)-4l_(2) ......... (4)`
From (1) & (3) `(l_(1)-l)/(l_(3)-l)=(4)/(9) rArr (l_(1)-(5l_(1)-4l_(2)))/(l_(3)-(5l_(1)-4l_(2)))=(4)/(9)`
`rArr (l_(1)-5l_(1)+4l_(2))/(l_(3)-5l_(1)+4l_(2))=(4)/(9) rArr (4l_(2)-4l_(1))/(l_(3)-5l_(1)+4l_(2))=(4)/(9)`
`rArr 36l_(2)-36l_(1)=4l_(3) -20l_(1)+16l_(2)`
`20l_(2)-16l_(1)=4l_(3) " "l_(3)=5l_(2)-4l_(1)`