Question

A cube is subjected to a uniform volume compression. If the side of the cube decreases by
2$\%$ , the bulk strain is:

• A. $0.02$
• B. $0.03$
• C. $0.04$
• D. $0.06$

Answer 1

The correct option is D $0.06$

Given. $\frac{\Delta a}{a}\times 100=2$ where a is side length of cube.

Bulk strain $=\frac{\Delta V}{V}$ Where $V$ is volume ef cube for cube $V=a^3$

differentiating both side w.r.t. V

$\begin{array}{cc}\frac{dv}{dv}& =\frac{d{a}^3}{dv}=\frac{d\left(a^3\right)}{da}\cdot \frac{da}{dv}\\ dv& =3a^2\cdot da\\ \frac{dv}{v}& =\frac{3a^{2}da}{a^3}=3\cdot \frac{da}{a}\\ \frac{\Delta v}{v}& =3x\frac{\Delta a}{a}\end{array}$

A putting values in this equationg $\frac{\Delta V}{V}=3\times \frac{2}{100}=0.06$