Question

The density $\rho$ of water of bulk modulus B at a depth y in the ocean is related to the density at surface ${\rho }_o$ by the relation

• A. $\rho ={\rho }_o[2+{\rho }_{o}gy/B]$
• B. $\rho ={\rho }_o[1+{\rho }_{o}gy/B]$
• C. $\rho =[2+{\rho }_{o}gy/B]$
• D. $\rho =[1+{\rho }_{o}gy/B]$

Answer 1

The correct option is B $\rho ={\rho }_o[1+{\rho }_{o}gy/B]$

$\begin{array}{c}Bulkmodulus,\\ B=-V_0\frac{\Delta p}{\Delta V}\Rightarrow \Delta V=-V_o\frac{\Delta p}{B}\\ \Rightarrow V=V_0\left[1-\frac{\Delta P}{B}\right]\\ \therefore Density\\ \rho ={\rho }_o{\left[1-\frac{\Delta p}{B}\right]}^{-1}={\rho }_o\left[1+\frac{\Delta p}{B}\right]\\ where,\Delta p=p-p_0=h{p}_{0}g\\ =pressuredifferencebetweendepthandsurfaceofocean\\ \therefore \rho ={\rho }_o\left[1+\frac{{\rho }_{0}gy}{B}\right]\left(ash=y\right)\end{array}$

Hence, the option $B$ is the correct answer.