Question

There is no change in the volume of a wire due to change in its length on stretching. The Poisson's ratio of the material of the wire is :

• A. $+0.50$
• B. $-0.50$
• C. $0.25$
• D. $-0.25$

Answer 1

The correct option is A $+0.50$

Let the material of length $l$ and side $s$

If a material maintains constant volume during stretching

$V=l\times s^2$

Differentiate wrt $dl$

$dV=s^2.dl+l.2s.ds$

$dl.s=2l.ds$

$\frac{ds}{dl}=-\frac{1}{2}\frac{s}{l}$

$\eta =-\frac{\frac{ds}{s}}{\frac{dl}{l}}=\frac{1}{2}$