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Question

# The density of water at the surface of the ocean is ρ. If the bulk modulus of water is B, what is the density of ocean water at a depth where the pressure is nP0, where P0 is the atmospheric pressure?

A

ρBB(n1)P0

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B

ρBB+(n1)P0

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C

ρBBnP0

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D

ρBB+nP0

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Solution

## The correct option is A ρBB−(n−1)P0 Pressure at the surface of the ocean =P0 Pressure at the given depth =nP0 ∴ Increase in pressure, ΔP=nP0−P0=(n−1)P0 Let V be the volume of a certain mass M of water at the surface, so that M=ρV. The decrease in volume under pressure ΔP is ΔV=VΔPB ∴ Volume of the same mass M of water at the given depth is V′=V−ΔV=V−VΔPB=V(1−ΔPB)=VB(B−ΔP) ∴ Density of water at that depth is ρ′=MV′=ρVV′=ρVVB(B−ΔP)=ρBB−ΔP=ρBB−(n−1)P0 Hence, the correct choice is (a).

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