Question

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 $10^{3} \,kg\, m ^{-3}$. 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. $1.4 \times 10^{-2}$

Answer 1

Answer: (C)

Given, $d=2700\, m$ and $\rho=10^{3}\, kg\,m ^{-3}$
Compressibility $=45.4 \times 10^{-11} \,Pa ^{-1}$
The pressure at the bottom of ocean is given by
$p=\rho g d=10^{3} \times 10 \times 2700=27 \times 10^{6} \,Pa$
So, fractional compression $=$ compressibility $\times$ pressure
$=45.4 \times 10^{-11} \times 27 \times 10^{6} $
$=1.2 \times 10^{-2}$