Question

A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by 1%. If the Poisson?s ratio for the material of the rod be 0.2, which of the following statements is correct ? "The volume approximately ....."

• A. decreases by 1%
• B. decreases by 0.8%
• C. decreases by 0.6%
• D. increases by 0.2%

Answer 1

Answer: (C)

decreases by 0.6%

Answer 2

$V=A\iota=ab\iota; \frac{\Delta a}{a}=\frac{\Delta b}{b}\left[\because\sigma=\frac{-\Delta\frac{a}{a}}{\Delta\frac{1}{1}}=\frac{\Delta\frac{b}{b}}{\Delta\frac{1}{1}}\right]$
$\Rightarrow\frac{\Delta V}{V}=2\frac{\Delta a}{a} +\frac{\Delta_{1}}{1} =-2\sigma\frac{\Delta_{1}}{1}+\frac{\Delta_{1}}{1} \Rightarrow\left(1-2\sigma\right)=-1\left(1-2\times0.2\right)=-1\left(1-0.4\right)=-0.6$