A wire is stretched such that its volume remains constant. The Poisson's ratio of the material of the wire is

Options

A. `0.25`
B. `0.50`
C. `-0.25`
D. `-0.50`

Answer

D

Explanation

`sigma =((Delta r)/( r))/( (Delta l)/( I))`
volume remain constant `V= Al implies +- (Delta V )/( V ) = +- (Delta A)/( A ) +- (Delta l )/(I) implies 0= ( 2Delta r)/( r ) +(Delta l )/( I)`
`((Delta r)/(r ))/(( Delta l)/(I)) = -1/2 =- 0.5`