Question

The density of water at the surface of the ocean is $\rho$ and atmospheric pressure is $p _{0}$. If the bulk modulus of water is $K$, what is the density of ocean water at a depth where the pressure is $n p_{0}$ ?

• A. $\frac{\rho k}{k-n p_{0}}$
• B. $\frac{\rho k}{k+n p_{0}}$
• C. $\frac{\rho k}{k-\left(n-1\right)p_{0}}$
• D. $\frac{\rho k}{k+\left(n-1\right)p_{0}}$

Answer 1

Answer: (C)

$\frac{\rho k}{k-\left(n-1\right)p_{0}}$

Answer 2

Variation of density with pressure is given by $\rho'$ $=\frac{\rho}{\left[1-\frac{\Delta p}{k}\right]}$ Here, $\Delta p$ $=np_{0}-p_{0}$ $=\left(n-1\right)p_{0}$ $\therefore\quad$ $\rho'$ $=\frac{\rho}{1-\frac{\left(n-1\right)p_{0}}{k}}$ $=\frac{\rho k}{k-\left(n-1\right)p_{0}}$