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

Question

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, + 1 2, - 1 2, + 1 4, - 1 4

MARKS App · Accepted Answer

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

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