# The Comprehensibility of water is $5 \times 10^{-10}\;m^2/N$. It is subjected to a pressure of $15\;M\;pa$. The fraction decrease in volume will be

$\begin {array} {1 1} (a)\;3.3 \times 10^{-5} \\ (b)\;5.6 \times 10^{-4} \\ (c)\;7.5 \times 10^{-3} \\ (d)\;1.5 \times 10^{-2} \end {array}$

compressibility $x=\large\frac{1}{k}$
Where $k$ is bulk modulus; $k=\large\frac{\Delta P}{\Large\frac{\Delta v}{v}}$
$\qquad= -\large\frac{- \Delta V}{v \Delta P}$
$\quad= 5 \times 10^{-10}$
$\therefore$ Fractional decrease in volume
$- \large\frac{\Delta v}{V}$$=x \Delta P$
$\qquad= 5 \times 10^{-10} \times 15 \times 10^6$
$\qquad= 7.5 \times 10^{-3}$