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_1F_1+L_2F_2)/(F_1+F_2)`
B. `(L_2-L_1)/(F_1+F_2)`
C. `(F_1L_2-F_2L_1)/(F_1-F_2)`
D. `(L_1F_1-F_2L_2)/(F_1-F_2)`

Answer

C

Explanation

let `L_(0)` be the original length,
`F_(1)=K(L_(1)-L_(0))`
`F_(2)=K(L_(2)-L_(0))`
` implies F_(1)/F_(2)=(L_(1)-L_(0))/(L_(2)-L_(0))`
`impliesF_(1)L_(2)-F_(1)L_(0)=F_(2)L_(1)-F_(2)L_(0)`
`impliesF_(1)L_(2)-F_(2)L_(1)=F_(1)L_(0)-F_(2)L_(0)`
`=L_(0)(F_(2)-F_(1))`
`therefore L_(0)=(F_(1)L_(2)-F_(2)L_(1))/(F_(1)-F_(2))`