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The density of water at the surface of o...

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

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)`

Text Solution

Verified by Experts

The correct Answer is:
A
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))`
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