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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(n1)P0


Pressure at the surface of the ocean =P0
Pressure at the given depth =nP0
Increase in pressure, ΔP=nP0P0=(n1)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=VΔV=VVΔPB=V(1ΔPB)=VB(BΔP)
Density of water at that depth is ρ=MV=ρVV=ρVVB(BΔP)=ρBBΔP=ρBB(n1)P0
Hence, the correct choice is (a).


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