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

Options

A. `0.8xx10^(-2)`
B. `1xx 10^(-2)`
C. `1.2xx10^(-2)`
D. `1.4 xx 10^(-2)`

Answer

C

Explanation

Given, d=2700m `rArr rho=10^(3) kgm^(-3)`
Compressibility `=45.4 xx 10^(-11)` per pascal
The pressure at the bottom of ocean is given be
`p=pgd=10^(3)xx 10 xx 2700=27 xx 10^(6)`Pa
So, fractional compression = compressibility x pressure
`=45.4 xx 10^(-11) xx 27 xx 10^(6)=1.2 xx 10^(-2)`