Question

The Poisson’s ratio of the 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 its length is

• A. 1%
• B. 2%
• C. 2.5%
• D. 4%

Answer 1

Answer: (D)

Given, Poisson’s ratio = 0.5. It shows that the density of material is constant. Therefore, the change in volume of the wire is zero. Thus
$V=A\times l=a$ constant
$\therefore \frac{\Delta V}{V}=\frac{\Delta A}{A}+\frac{\Delta l}{l}=0$ or $\frac{\Delta l}{l}=-\frac{\Delta A}{A}$
or $\%$ increase in length $=\frac{\Delta l}{l}\times 100=-\left(4\right)=4\%$