For which value of Poisson's ratio the volume of a wire does not change when it is subjected to a tension ?

Options

A. -0.5
B. 0.5
C. 0.1
D. 0

Answer

2

Explanation

`v=pi r^(2)L`
`dv=pi r^(2)dl+L 2pi rdr`
As v is constant
`therefore dv=0`
`0=pi r^(2) dl+2pi rLdr`
`pi r^(2)dl=-2pi rLdr`
`dl=-2L(dr)/(r )`
`(dl)/(L)=-2 (dr)/(r )`
`-(1)/(2) =(dr//r)/((dl)/(2))=-sigma`
`therefore =0.5`.