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  • The Poisson's ratio of a material is 0.4 . If a force is applied to a wire of this material, there is a decrease of cross-sectional area by <img alt="2 \%" src="https://entrancecorner.oncodecog

The Poisson's ratio of a material is 0.4 . If a force is applied to a wire of this material, there is a decrease of cross-sectional area by 2 \%. The percentage increase in its length is:

Option: 1

3 \%


Option: 2

2.5 \%


Option: 3

1 \%


Option: 4

0.5 \%


Answers (1)

Poisson's ratio is defined as

                \mathrm{ \sigma=\frac{\Delta d / d}{\Delta l / l} \quad \text { or } \quad \frac{\Delta l}{l}=\frac{\Delta d / d}{\sigma} }
where d is the diameter and l is the length of the wire. The area of cross-section is

                 \mathrm{ A=\pi r^2=\frac{\pi d^2}{4} }
or       \mathrm{\quad \log A=\log \left(\frac{\pi}{4}\right)+2 \log d}

Differentiating, we have

\mathrm{ \begin{gathered} \frac{\Delta A}{A}=2 \frac{\Delta d}{d} \\\\ \text { or } \quad \frac{\Delta d}{d}=\frac{1}{2} \frac{\Delta A}{A}=\frac{1}{2} \times 2 \%=1 \% \\\\ \left(\because \frac{\Delta A}{A}=2 \%, \text { given }\right) \end{gathered} }

Using this in (i) we have
 

\mathrm{ \frac{\Delta l}{l}=\frac{1 \%}{0.4}=2.5 \% \quad(\because \sigma=0.4) }

Posted by

Ramraj Saini

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