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

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