Question

The Bulk Modulus for an incompressible liquid is

• A. zero
• B. unity
• C. infinity
• D. between $ 0 $ and $ 1 $

Answer 1

The Correct Option is C

The bulk modulus is
$B=-\frac{PV}{\Delta V}$
If liquid is incompressible, so
$\Delta V=0$
Hence, $B =-\frac{pV}{0}=\infty$
$\Rightarrow B=\infty$ (infinity)

Answer 2

Given that the liquid is incompressible, the volume of any incompressible liquid does not change.
The bulk modulus is a measure of the resistance that anybody gives to compressive force applied to it.
Bulk modulus is defined mathematically as the ratio of normal stress to volumetric strain, or, in a more basic form, the ratio of infinitesimal change in pressure to relative volume reduction.
The bulk modulus is represented by K, and is given by 
\(K=\frac{\frac{F}{A}}{\frac{\Delta V}{V}}\) or \(K=\frac{\Delta P}{\frac{\Delta V}{V}}\)
As for any incompressible liquid, the ΔV will be approximately equal to zero.
\(K=\frac{\Delta P}{\frac{0}{V}}\)
\(K=\frac{\Delta P}{0}\)
As a result, everything divided by zero yields infinite.
As a result, K=\(∞\) indicating that the incompressible fluid will completely withstand the compressive force applied to it.