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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 :
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$4 \%$
Poisson ratio $=0.5$
Therefore density is constant hence change in volume is zero we have $\mathrm{V}=\mathrm{A} \times \ell=$ constant
$\log \mathrm{V}=\log \mathrm{A}+\log \ell$ or $\frac{d A}{A}+\frac{d \ell}{\ell}=0 \Rightarrow \frac{d \ell}{\ell}=-\frac{d A}{A}$
That is $4 \%$
Therefore density is constant hence change in volume is zero we have $\mathrm{V}=\mathrm{A} \times \ell=$ constant
$\log \mathrm{V}=\log \mathrm{A}+\log \ell$ or $\frac{d A}{A}+\frac{d \ell}{\ell}=0 \Rightarrow \frac{d \ell}{\ell}=-\frac{d A}{A}$
That is $4 \%$
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