Question

A liquid of bulk modulus $k$ is compressed by applying an external pressure such that its density increases by $0.01$%. The pressure applied on the liquid is:

• A. $\frac{k}{10000}$
• B. $\frac{k}{1000}$
• C. $1000k$
• D. $0.01k$

Answer 1

The correct option is A $\frac{k}{10000}$

Bulk modulus is given by:

$k=-\frac{P}{\frac{\Delta V}{V}}\Rightarrow \frac{P}{k}=-\frac{\Delta V}{V}=\frac{\Delta \rho }{\rho }$
$P=k\frac{\Delta \rho }{\rho }=\frac{k}{10000}$