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Q.
A uniform cubical block is subjected to volumetric compression, which decreases its each side by $2\%$. The Bulk strain produced in it is
Mechanical Properties of Solids
Solution:
Volume $=(\text { side })^{3}$
$v=(a)^{3}$
So $\frac{\Delta V}{V}=\frac{3 \Delta a}{a}$
$\left\{\right.$ given $\left.\frac{\Delta a}{a}=-2 \%\right\}$
$\therefore \frac{\Delta V}{v}=3 \times-2$
Side decreases so we used (-)ve sign
$=-6 \%$
We know
$\frac{\Delta v}{V}=-\frac{P}{B}$
Substituting value of $\Delta v / v$
$-\frac{6}{100}=-\frac{P}{B}$
So bulk strain produced is $0.06$