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=FlaΔlY, I and a are constants∴ FlΔl= constant or Δl∝F Now, l1−l=T1 and l2−l=T2 Dividing, l1−ll2−l=T1T2or  l1T2−lT2=l2T1−lT1 or lT1−T2=l2T1−l1T2or  l=l2T1−l1T2T1−T2  or l=l1T2−l2T1T2−T1