Question

The density of water at the surface of the ocean is p. If the bulk modulus of water is B, what is the density of ocean water at a depth where the pressure in $n{p}_0$, where $P_0$ is the atmospheric pressure

• A. $\frac{\rho B}{B-(n-1)P_0}$
• B. $\frac{\rho B}{B+(n-1)P_0}$
• C. $\frac{\rho B}{B-n{P}_0}$
• D. $\frac{\rho B}{B+n{P}_0}$

Answer 1

The correct option is A $\frac{\rho B}{B-(n-1)P_0}$

$B=-V\frac{dP}{dV}$

Thus, $\Delta V=-\frac{P_0(n-1)V}{B}$ or $V^{\prime }-V=-\frac{P_0(n-1)V}{B}$ or, $V^{\prime }=V(1-\frac{P_0(n-1)}{B})$

Now, ${\rho }^{\prime }=\frac{m}{V^{\prime }}=\frac{m}{V(1-\frac{P_0(n-1)}{B})}=\frac{\rho }{(1-\frac{P_0(n-1)}{B})}=\frac{\rho B}{(B-P_0(n-1\left)\right)}$