The length of a metal wire is l1 when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is

As, Young's modulus of elasticity,  Y= Stress  Strain ⇒ Y=T1×LA×I1−L  .... (i)where, L is the original length of the wire and alsoY=T2×LA×I2−L …. (ii) From Eqs. (i) and (ii), we getT1LAI1−L=T2LAI2−L⇒L=T2I1−T1I2T2−T1