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  4. 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

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Q. 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

Mechanical Properties of Solids

Solution:

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
$V = A × l = a$ 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 $=\frac{\Delta l}{l}\times100=-\left(4\right)=4\%$