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Q.

The density $ρ$ of water of bulk modulus $B$ at a depth $y$ in the ocean is related to the density at surface $ρ_{0}$ by the relation

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a

$ρ = ρ_{0} [1 - \frac{B}{ρ_{0} h g y}]$

b

$ρ = ρ_{0} [1 + \frac{ρ_{0} g y}{B}]$

c

$ρ = ρ_{0} [1 + \frac{B}{ρ_{0} h g y}]$

d

$ρ = ρ_{0} [1 - \frac{ρ_{0} g y}{B}]$

answer is B.

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Detailed Solution

$\begin{array}{l} Bulk modulus, B = - V_{0} \frac{Δ P}{Δ V} \\ \Rightarrow Δ V = - V_{0} \frac{Δ P}{B} \\ \Rightarrow V = V_{0} [1 - \frac{Δ P}{B}] \\ ∴ Density, ρ = ρ_{0} {[1 - \frac{Δ P}{B}]}^{- 1} = ρ_{0} [1 + \frac{Δ P}{B}] \\ here, Δ P = P - P_{0} = h ρ_{0} g \\ ∴ ρ = ρ_{0} [1 + \frac{ρ_{0} g y}{B}] (As h = y) \end{array}$

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