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

Options

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

Answer

C

Explanation

As, `F alpha Deltal "where", Deltal`=change in length Now, suppose the origin length of the metal wire is l then, `F_(1)prop(l_(1)-l)`
`similarly, F_(2)prop(l_(2)-l)`
The ratio, `(F_1)/(F_2)=(l_1-l)/(l_2-l)`
`Rightarrow F_(1)l_(2)-F_(1)l=F_(2)l_(1)-F_(2)l`
`Rightarrow (F_(2)-F_(1))l=F_(2)l_(1)-F_(1)l_(2)`
`Rightarrow l=(F_(2)l_(1)-F_(1)l_(2))/(F_(2)-F_(1))`