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

Determine the poisson's ratio of the material of a wire whose volume r

1.	Determine the poisson's ratio of the material of a wire whose volume remains constant under an external normal stress.
Answer» Solution :Let l, D be the LENGTH and DIAMETER of the given wire RESPECTIVELY. As volume of wire remains constant. So`(piD^(2)l)/(4)=a"constant"""...(1)` Differentiating it, we have, `(pi)/(4)(2DDeltaDxxl+D^(2)Deltal)=0` DIVIDING it by `D^(2)l` we GET `(2DeltaD)/(D)+(Deltal)/(l)=0` (or)`(Deltal)/(l)=-(2DeltaD)/(D)` `sigma=(-DeltaD//D)/(Deltal//l)=(-DeltaD//D)/(-(2DeltaD//D))=(1)/(2)` `=0.5`