Question

The Poisson?? 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. 0.01
• B. 0.02
• C. 0.025
• D. 0.04

Answer 1

Answer: (D)

0.04

Answer 2

Given, Poisson?? ratio = 0.5. It shows that the density of material is constant. Therefore, the change in volume of the wire is zero. Thus $V = A ? l = a$ 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 $=\frac{\Delta l}{l}\times100=-\left(4\right)=4\%$