Q140 / 160 · WBJEE 2009 · Physics

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
    $1 \%$
  • B
    $2 \%$
  • C
    $2.5 \%$
  • Correct answer
    D
    $4 \%$

Solution

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 $4 \%$

Hence, the correct answer is option: 'D'.

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