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. 1000 k
• D. 0.01 k

Answer 1

Answer: (A)

$\frac{k}{10000}$

Answer 2

$k = \frac{P}{\Delta v/v } \Rightarrow \frac{P}{k} = \frac{\Delta V}{V} = \frac{\Delta\rho}{\rho}$
$\Rightarrow\,P = \frac{k\Delta\rho}{\rho} = \frac{k}{1000}$