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. 0.01
• B. 0.02
• C. 0.025
• D. 0.04

Answer 1

Answer: (D)

0.04

Answer 2

Poisson's ratio $=0.5$
Since, density is constant therefore change in volume is zero, we have
$V = A \times 1=$ constant
$\log V=\log A+\log 1$
or $\frac{ d A }{ A }+\frac{ dl }{ l }=0$
$\frac{ d l }{ l }=-\frac{ d A }{ A }$
$\therefore$ Percentage increase in length $=4 \%$