The length of a metal wire is `l_(1)` when the tension in it is `F_(1)` and `l_(2)` when the tension becomes `F_(2)`. Find the natural length of wire.

Explanation

Suppose L be the natural legth of the wire
We have Y`=(FL)/(ADeltaL)`
In the first case ,`F=T_1 DeltaL=L_1-L`
`Y=(T_1L)(A(L_1-L)`
In the second case ,`F=T_2,DeltaL=L_2-L`
`Y=(T_2L)/(A(L_2-L))`
for equation (i) and(ii),We get
`(T_1L)/(A(L_1-L))=(T_2L)/(A(L_2-L))`
or,`T_1(L_2-L)=T_2(L_1-L)`
or`L(T_2-T_1)=L_1T_2-L_2T_1`
`L=(L_1T_2-L_2T_1)/)(T_2-T_1)`