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The approximate depth of an ocean is 270...

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?

A

`0.8 xx 10^(-2)`

B

`1.0 xx 10^(-2)`

C

`1.2 xx 10^(-2)`

D

`1.4 xx 10^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
c
Given `d = 2700m rArr rho = 10^(3)kg//m^(3)`
Compressibility `= 45.4 xx 10^(-11)` per pascal
The pressure at the bottom of ocean is given by
`p = rho gd = 10^(3) xx 10 xx 2700 = 27 xx 10^(6) Pa`
So, fractional compression = compressibility `xx` pressure
`= 45.4 xx 10^(-11) xx 27 xx 10^(6) = 1.2 xx 10^(-2)`
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