When the tension in a metal wire is T1, its length is l1. When the tension is T2, its length is l2. The natural length of wire is
Y=FlA△ l
Y, l and A are constants
Therefore F△ l=costant or △ l ∝ F
Now, l1−l∝ T1 and l2−l∝ T2
Dividing,l1−ll2−l=T1T2
or l1T2−lT2=l2T1−lT1
or l(T1−T2)=l2T1−l1T2
or l=l2T1−l1T2T1−T2
or l=l1T2−l2T1T2−T1