Question

The Poisson's ratio of a material is $0.5$. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by $4\%$. The percentage increase in the length is:

• A. $1\%$
• B. $2\%$
• C. $2.5\%$
• D. $4\%$

Answer 1

The correct option is D $4\%$

Poisson's ratio $=0.5$
Since, density is constant therefore change in volume is zero, we have
$V=A\times l=constant$
$\log V=\log A+\log l$
or $\frac{dA}{A}+\frac{dl}{l}=0$
$\frac{dl}{l}=-\frac{dA}{A}$
$\therefore$ Percentage increase in length = $4\%$