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)

. 4%.

Given Poisson's ration= 0.5

It shows that the density of material is constant
Therefore the change in volume of the wire is zero
Thus
$V=A\times l$ = constant
therefore $\frac{△V}{V}=0=\frac{△A}{A}+\frac{△l}{l}$
$\frac{△l}{l}=-\frac{△A}{A}$
or % increase in length=$\frac{△l}{l}\times 100$
=-(-4)
=4%