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The approximate depth of an ocean is 270...

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

A

`0.8 times 10^-2`

B

`1.0 times 10^-2`

C

`1.2 times 10^-2`

D

`1.4 times 10^-2`

Text Solution

Verified by Experts

The correct Answer is:
C
Due to `Delta P` amount of increase in pressure, there is `DeltaV` amount of compression in volume V.
So, fractional compression =`(DeltaV)/V`
And compressibility, `K-1/V(DeltaV)/P`
Now consider the magnitude, `(DeltaV)/V=K Delta P`
Here, `Delta P=h rho g=2700 times 10^3 times 10 Pa`
Hence, fractional compression,
`(DeltaV)/V=(45.4times10^-11)times(2700times10^3times10)`
`=1.226 times 10^-2`
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