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. `(pB)/(B-(alpha-1)p_(0))`
B. `(pB)/(B+(alpha-1)p_(0))`
C. `(pB)/(B-alphap_(0))`
D. `(pB)/(B+alphap_(0))`

Answer

A

Explanation

From the definition of bulk modulus `B=-(dp)/(dV//V)`
As we move from surface to placed where pressure changes to `alphap_(0)`. Let us assume volume changes by `/_\V` then.
`B=(V/_\p)/(/_\V)=(V(alpha-1)p_(0))/(/_\V)`
New volume `V'=V-/_\V=V[1-((alpha-)p_(0))/B]`
Density at the given depth `rho'=rhoV//V` where `rho` is density at surface
`rho'=(rhoxxB)/(B-(alpha_(1))rho_(0))`