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?
AIPMT 2015, Medium
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Depth of ocean $d = 2700\,m$
Density of water, $\rho = {10^3}\,kg\,{m^{ - 3}}$
Compressibility of water, $K = 45.4 \times {10^{ - 11}}P{a^{ - 1}}$
$\frac{{\Delta V}}{V} = ?$
Excess pressure at the bottom, $\Delta P = \rho gd$
$ = {10^3} \times 10 \times 2700 = 27 \times {10^6}Pa$
$We\,know,\,B = \frac{{\Delta P}}{{\left( {\Delta V/V} \right)}}$
$\left( {\frac{{\Delta V}}{V}} \right) = \frac{{\Delta P}}{B} = K.\Delta P$ $\left( {K = \frac{1}{B}} \right)$
$ = 45.4 \times {10^{ - 11}} \times 27 \times {10^6} = 1.2 \times {10^{ - 2}}$
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