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_(1)+F_(2))`
C. `(F_(1)L_(1)-F_(1)L_(1))/(F_(1)-F_(2))`
D. `(F_(1)L_(1)-F_(2)L_(2))/(F_(1)-F_(2))`

Explanation

Change in length of wire of length L is directly proportional to the external force applied

`F_(1)prop(L_(1)-L)`
`rArr " " F_(1) = K (L_(1) - L)`
Similarly, `F_(2) = K (L_(2) - L)`
Dividing Eq. (i) by Eq. (ii), we get
`(F_(1))/(F_(2))=(L_(1)-L)/(L_(2)-L)`
`rArr F_(1)L_(2)-F_(1)L=F_(2)L_(1)-F_(2)L`
`rArr " " L=(F_(1)L_(2)-F_(2)L_(1))/(F_(1)-F_(2))`