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

Answer: (D)

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
$\frac{dv}{dv}=\frac{d{a}^3}{dv}=\frac{d\left(a^3\right)}{da}\cdot \frac{da}{dv}$
$dv=3a^2\cdot da$
$\frac{dv}{v}=\frac{3a^{2}da}{a^3}=3\cdot \frac{da}{a}$
$\frac{\Delta v}{v}=3x\frac{\Delta a}{a}$
A putting values in this equationg
$\frac{\Delta V}{V}=3\times \frac{2}{100}=0.06$