The density of water at the surface of ocean is `rho` . If the bulk modulus of water is `B`, then the density of ocean water at depth, when the pressure at a depth is `alphap_(0)` and `p_(0)` is the atmospheric pressure is

Options

A. `(rho B)/(B - (n - 1)P_(0))`
B. `(rho B)/(B + (n - 1)P_(0))`
C. `(rho B)/(B - nP_(0))`
D. `(rho B)/(B + nP_(0))`

Answer

A

Explanation

Increases in pressure
`(Delta P) = nP_(0) - P_(0) = (n-1) P_(0)`
From `M = rho V`, the decrases in volume due to increases in pressure `Delta P` is `Delta V = (V Delta P)/(B)`
`V = V-Delta V = V - (V Delta P)/(B) = (V)/(B) (B- Delta P)`
`rho = (M)/(V) = (rho V)/(V)`