When the tension in a metal wire is `T_(1)`, its length is `I_(1)`. When the tension is `T_(2)`, its length is `I_(2)`. The natural length of wire is

Options

A. `sqrt(l_(1)l_(2)`
B. `(l_(1)+l_(2))/(2)`
C. `((l_(1)T_(2)-l_(2)T_(1)))/(T_(2)-T_(1))`
D. `(l_(1)T_(2)-l_(1)T_(2))/(T_(1)-T_(2))`

Answer

C

Explanation

Let unstrethched length = I
`T_(1)=K(l_(1)- l) rArr T_(2)= k(l_(1)-l)`
`(T_(1))/(T_(2))= (l_(1)-l)/(l_(2)-l) rArrl= ((T_(2)l_(1)-T_(1)l_(2))/(T_(2)- T_(2)))`