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

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Solution

The correct option is B

Bulk modulus, $B = - V_{0} \frac{Δ p}{Δ V} \Rightarrow Δ V = - V_{0} \frac{Δ p}{B}$

$\Rightarrow V = V_{0} [1 - \frac{Δ p}{B}]$

$∴ D e n s i t y, ρ = ρ_{0} {[1 - \frac{Δ p}{B}]}^{- 1} = ρ_{0} [1 + \frac{Δ p}{B}]$

where, $Δ p = p - p_{0} = h p_{0} g$

= pressure difference between depth and surface of ocean

$∴ ρ = ρ_{0} [1 + \frac{ρ_{0} g y}{B}] (A s h = y)$

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

The correct option is B Bulk modulus, B=−V0ΔpΔV⇒ΔV=−V0ΔpB ⇒V=V0[1−ΔpB] ∴Density, ρ=ρ0[1−ΔpB]−1=ρ0[1+ΔpB] where, Δp=p−p0=hp0g = pressure difference between depth and surface of ocean ∴ρ=ρ0[1+ρ0gyB] (As h=y)

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