Estimate the change in density of ocean water at a depth of 400 m below the surface. Given: surface density rho₀ = 1030 kg/m³, bulk modulus of water B = 2 x 10⁹ N/m², and g = 10 m/s².

(A) 2.1 kg/m³
(B) 0.21 kg/m³
(C) 21 kg/m³
(D) 0.021 kg/m³

Correct answer: (A) 2.1 kg/m³

Solution

The pressure at 400 m is P = 1030 x 10 x 400 = 4.12 x 10⁶ Pa. Using drho = rho₀ * dP / B = 1030 x 4.12 x 10⁶ / (2 x 10⁹) approximately 2.12 kg/m³ approximately 2.1 kg/m³.

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