Question

Find the volumetric strain of the spherical ball of radius $10\text{cm}$ whose volume changes by $4.18\times {10}^{-6}{\text{m}}^3$ under the application of bulk stresses.

• A. $1.0$
• B. $0.1$
• C. $0.01$
• D. $0.001$

Answer 1

The correct option is D $0.001$

As we know,
Volumetric strain is the ratio of change in volume of the body to the original volume.
Volumetric strain $=\frac{\Delta V}{V}$ ...$\left(i\right)$
Where $△V=$change in volume$=4.18\times {10}^{-6}{m}^3$

volume of sphere, $\left(V\right)=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \pi \times (0.1{)}^3$
$=4.18\times {10}^{-3}{\text{m}}^3$
from equation $\left(i\right)$,
$\text{volumetric strain}=\frac{4.18\times {10}^{-6}}{4.18\times {10}^{-3}}={10}^{-3}$