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)

When strain is small the ratio of the normal stress to the volume strain is called the bulk modulus of the material of the body.
$B =\frac{\text { normal stress }}{\text { volume strain }}$
$B =-\frac{\Delta P}{\Delta V / V}$
$B \propto \frac{1}{\frac{\Delta V}{V}}$
$\Rightarrow \frac{\Delta V}{V} \propto \frac{1}{B}$