The density of water at the surface of the ocean is `rho` and atmospheric pressure is `P_(0)` If the bulk modulus of water is K, what is the density of ocean water at a depth where the pressure is `nP_(0)`?

Options

A. `(rhoB)/(B-(n-1)P_(0))`
B. `(rhoB)/(B+(n-1)P_(0))`
C. `(rhoB)/(B-nP_(0))`
D. `(mu(v_(e)-gt))/(2M-mut)`

Answer

A

Explanation

Pressure at the surface of the ocean the =`P_(0)`, atmospheric pressure.
Pressure at a depth `=nP_(0)"(given)."`
Increase in pressure `(triangleP)=nP_(0)-P_(0)=(n-1)P_(0)`
Let V be the volume of a certain mass M of water at the surface, so that `M=rhov`
The decrease in volume under increased pressure `(triangleP)=triangleV=(VtriangleP)/(B)`
Volume of the same mass M of water at the given depth is `V'=V-triangleV=V-(V triangleP)/(B)=V(1-(triangleP)/(B))=V/B (B-triangleP)`
Density of water at the depth is `rho'=M/V=(rhov)/(V')=(rhoV)/((V/B(B-triangleP))=(rhoB)/(B-triangleP)=(rhoB)/(B-(n-1)P_(0))`