Question

For a constant hydraulic stress on an object, the fractional change in the object's volume ($\Delta V/V$) and its bulk modulus (B) 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

Answer: (B)

$\frac{\Delta V}{V}\propto \frac{1}{B}$

$B=\frac{stress}{volumestrain}=\frac{stress}{\frac{\Delta V}{V}}$

$\frac{\Delta V}{V}=\frac{stress}{B}$

As stress is constant

$\frac{\Delta V}{V}\propto \frac{1}{B}$