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

$\text{Compressibility}=\frac{1}{\text{Bulk modulus}}$
$=45.4\times {10}^{-11}{\mathrm{Pa}}^{-1}$

$\text{Pressure}=2700\times 10\times {10}^3(\text{as}\mathrm{P}=\mathrm{hdg})$

$=27\times {10}^6$

According to definition of Bulk modulus,

$B=\frac{P}{\frac{-\mathrm{\Delta }V}{V}}$

Then, fractional change in volume

$\frac{\mathrm{\Delta V}}{\mathrm{V}}=\frac{\mathrm{P}}{\mathrm{B}}=\mathrm{P}\times \text{compressibility}$
$\text{As, compressibility}=45.4\times {10}^{-11}{\mathrm{Pa}}^{-1}$
$\text{So,}\frac{\mathrm{\Delta }v}{v}=27\times {10}^6\times 45.4\times {10}^{-11}$
$=1225.8\times {10}^{-5}=1.2\times {10}^{-2}$