WBJEE · Physics · Mechanical Properties of Solids
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 \(2.5 \%\)
- D \(4 \%\)
Answer & Solution
Correct Answer
(D) \(4 \%\)
Step-by-step Solution
Detailed explanation
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 \(\frac{d A}{A}+\frac{d \ell}{\ell}=0 \Rightarrow \frac{d \ell}{\ell}=-\frac{d A}{A}\)…
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