The density $p$ of water of bulk modulus B at a depth y in …

Physics Fluid Mechanics Pressure and Density Single Correct MCQ

Published on: September 12, 2026

The density $p$ of water of bulk modulus B at a depth y in the ocean is related to the density at surface $p_0$ by the relation

$\rho = \rho_0 \left[ 1 - \frac{\rho_0 g y}{B} \right]$

$\rho = \rho_0 \left[ 1 + \frac{\rho_0 g y}{B} \right]$

$\rho = \rho_0 \left[ 1 + \frac{B}{\rho_0 h g y} \right]$

$\rho = \rho_0 \left[ 1 - \frac{B}{\rho_0 g y} \right]$

Text Solution

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The correct answer is:

Bulk modulus, $B = -V_0 \frac{\Delta p}{\Delta V} \Rightarrow \Delta V = -V_0 \frac{\Delta p}{B}$

⇒ ⇒ $v = v_0 \left[ 1 - \frac{\Delta p}{B} \right]$

∴ ∴ Density, $\rho = \rho_0 \left[ 1 - \frac{\Delta p}{B} \right]^{-1} = \rho_0 \left[ 1 + \frac{\Delta p}{B} \right]$

where, $\Delta p = p - p_0 = h \rho_0 g$

= pressure difference between depth and surface of ocean

∴ ∴ $\rho = \rho_0 \left[ 1 + \frac{\rho_0 g y}{B} \right]$ (As h = y)

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