Determine the poisson's ratio of the material of a wire whose volume remains constant under an external normal stress.

Explanation

Volume of a wire, `V=pi(D^2)/(4)l`
As volume remains constant, the differentiation of the above equation gives,
`0=(pil)/(4)2DdD+(piD^2)/(4)dl`
(or) `-2ldD=Ddl`
(or) `(dD)/(D)=-(1)/(2)(dl)/(l)`
By definition, Poisson's ratio is
`sigma=(-dD//D)/(dl//l)=((1)/(2)(dl)/(l))/(dl//l)=(1)/(2)=0.5`