Question

For a constant volumetric stress on an object, the fractional change in the object volume $\left(\frac{\Delta V}{V}\right)$ and its bulk modulus $\left(B\right)$ are related as

• A. $\frac{\Delta V}{V}\propto B$
• B. $\frac{\Delta V}{V}\propto \frac{1}{B}$
• C. $\frac{\Delta V}{V}\propto B^2$
• D. $\frac{\Delta V}{V}\propto B^{-2}$

Answer 1

The correct option is B $\frac{\Delta V}{V}\propto \frac{1}{B}$

As we know,
Bulk Modulus $=\frac{\text{Volumetric stress}}{\text{Volumetric strain}}$
So, $B=\frac{\Delta P}{\Delta V/V}$

Given,
Volumetric stress $\Delta P=$ constant
$\Rightarrow \frac{\Delta V}{V}\propto \frac{1}{B}$