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?
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).