The length of a metal wire is `l_1` when the tensionin it is `T_1 and is l_2` when the tension is `T_2`. The natural length of the wire is

Options

A. `(T_2)/(T_1)(l_1+l_2)`
B. `T_2l_1+T_2l_2`
C. `(l_1T_2-l_2T_1)/(T_2-T_1)`
D. `(l_1T_2+l_2T_1)/(T_2+T_1)`

Answer

C

Explanation

`Y=(Fl)/(atrianglel)`
`Y`, `l` and `a` are constants
`(Fl)/(trianglel)=`constant or `trianglelpropF`
Now, `l_1lpropT_1` and `l_2-lT_2`
Dividing, `(l_1-1)/(l_1-1)=(T_1)/(T_2)`
or `l_1T_2-lT_2=l_2T_1-lT_1`
or `l(T_1-T_2)=l_2T_1-l_1T_2`
or `l=(l_1T_2-l_1T_2)/(T_1-T_2)` or `l=(l_1T_2-l_2T_1)/(T_3-T_1)`