There is no change in the volume of a wire due to the change in its length on stretching. The Poisson's ratio of the material of the wire is

Step-by-step solution

Volume of cylindrical wire, V = πr 2 L 4 , where x is the diameter of wire. Differentiating both sides, dV dx = π 4 2 xL + x 2 ⋅ dL dx Also, volume remains constant ∴    dV dx = 0 ∴      2 xL + x 2 dL dx = 0 ⟹    2 xL = - x 2 dL dx ⟹    dx x dL L = - 1 2 Poisson's ratio = - 1 2