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) \(1000 \mathrm{k}\)
(D) \(0.01 \mathrm{k}\)

Answer 1

Ans(A)

\(\mathrm{k}=-\frac{\mathrm{P}}{\Delta \mathrm{V} / \mathrm{v}} \Rightarrow \frac{\mathrm{P}}{\mathrm{k}}=-\frac{\Delta \mathrm{V}}{\mathrm{V}}=\frac{\Delta \rho}{\rho}\)

\(\Rightarrow P=\frac{k \Delta \rho}{\rho}=\frac{k}{10000}\)