The approximate depth of an ocean is `2700m`. The compressibility of water is `45.4xx10^(-11)Pa^-1` and density of water is `10^3(kg)/(m^3)`. What fractional compression of water will be obtained at the bottom of the ocean?

Options

A. `1.0xx10^(-2)`
B. `1.2xx10^(-2)`
C. `1.4xx10^(-2)`
D. `0.8xx10^(-2)`

Answer

B

Explanation

Here, `h=2700m,k=45.4xx10^(-11) Pa^(-1)`,
`rho=10^(3) kg//m^(3)`
As `B=(P)/(Delta V//V)` or `(Delta V)/(V)=(P)/(B)`
As `P=(F)/(A)=(mg)/(A)=(Vxxrhoxxg)/(A)=h rho g`
Also `B=(1)/(k)`
or `(Delta V)/(V)=Pk=h rho g k`
`=2700xx10^(3)xx9.8xx45.4xx10^(-11)`
`=1201284xx10^(3)xx10^(-11)`
`=1201284xx10^(-8) =1.2xx10^(-2)`