If the volume of a wire remains constant when subjected to tensile stress, the value of Poisson's ratio of the material of the wire is

Let L be the length, r be the radius of the wire.Volume of the wire is      V = πr2LDifferentiating both sides, we get∆V = π(2r∆r)L+πr2∆LAs the volume of the wire remains uncharged when it gets stretched, so ∆V=0. Hence0 = 2πrL∆r + πr2∆L∴  ∆rr∆LL = -12Poisson's ratio = Lateral strainLongitudinal strain                       = -∆rr∆LL = 12 = 0.5