The length of a metal wire is `l_(1)` when the tension in it is `T_(1)` and is `l_(2)` when the tension is `T_(2)`. The natural length of the 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_(2)T_(1))/(T_(1)+T_(2))`

Answer

C

Explanation

Let l be the original length and A be the area of cross-section of the wire.
change is length in first case `=l_(1)-l`
change in length in second case `=l_(2)-l`
`Y=(T_1)/(A).(l)/(l_(1)-l)=(T_2)/(A).(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))`