Question

A wire, of length L and radius r, is subjected to a (longitudinal) force F that causes its length to increase by an amount ΔL. Assuming that the total volume of the wire remains unchanged even after this increase in its length, the Poisson’s ratio, of the material of the wire, equals

(1) (1/2)

(2) (2/3) 

(3) (3/4)

(4) (4/5)

Answer 1

(1) (1/2)

The (original) volume of the wire is

V = πr²l

When the length of the wire increases by an amount Δl , its radius must decrease (say, by an amount Δr ) so that the volume still equals V. We thus have

The Poisson’s ratio, σ , is given by