Question

The approximate depth of an ocean is 2700m. The compressibility of water is $45.4\times {10}^{-11}P{a}^{-1}$ 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. $1.4\times {10}^{-2}$
• B. $0.8\times {10}^{-2}$
• C. $1\times {10}^{-2}$
• D. $1.2\times {10}^{-2}$

Answer 1

The correct option is D

$1.2\times {10}^{-2}$

Bulk modulus $=\frac{I}{K}$
$=\frac{1}{K\left(compressibilityfactor\right)}=\frac{1}{45.5\times {10}^{-11}}B=\frac{P}{-\frac{\Delta V}{V}}P=h\ell g\frac{\Delta V}{V}=\frac{P}{B}=\frac{h\ell g}{B}=\frac{2700\times {10}^3\times 10}{\frac{1}{45.4\times {10}^{-11}}}\frac{\Delta V}{V}=2700\times {10}^4\times 45.4\times {10}^{-11}=1.22\times {10}^{-2}$