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The length of a metal wire is L1 when the tension is T1 and L2 when the tension is T2. The unstretched length of wire is

  • L1 + L22

  • L1L2

  • T2L1 - T1L2T2 - T1

  • T2L1 + T1L2T2 + T1


T2L1 - T1L2T2 - T1

Let the initial length of the metal wire is L.

The strain at tension T1 is ΔL1 = L1 − L

The strain at tension T2 is ΔL2 = L2 − L

Suppose, the Young's modulus of the wire is Y, then

    T1AL1L = T2AL2L

where, A is an cross-section of the wire, assume to be same at all the situations

 T1A × LL1 = T2A × LL2      T1L1 - L = T2L2 - L  T1 L2 - L  = T2 L1 - L                L    = T2L1 - T1L2T2 - T1