The fractional compression $\left( \frac{\Delta V}{V} \right)$ of water at the depth of 2.5 km below the sea level is __________ %. Given, the Bulk modulus of water = $2 \times 10^9$ N m$^{-2}$, density of water = $10^3$ kg m$^{-3}$, acceleration due to gravity $g = 10$ m s$^{-2}$.

<p>The fractional compression $\left( \frac{\Delta V}{V} \right)$ of water at a depth of 2.5 km below sea level is calculated as follows:</p> <p>Given:</p> <p><p>Bulk modulus of water, $B = 2 \times 10^9 \, \text{N/m}^2$</p></p> <p><p>Density of water, $\rho = 10^3 \, \text{kg/m}^3$</p></p> <p><p>Acceleration due to gravity, $g = 10 \, \text{m/s}^2$</p></p> <p>The relationship between pressure change and volume change using the bulk modulus is given by:</p> <p>$ B = \frac{\rho gh}{\left(\frac{\Delta V}{V}\right)} $</p> <p>Rearranging the formula to solve for the fractional compression:</p> <p>$ \frac{\Delta V}{V} \times 100 = \frac{\rho gh}{B} \times 100 $</p> <p>Substituting in the given values:</p> <p>$ \frac{1000 \times 10 \times 2.5 \times 10^3}{2 \times 10^9} \times 100\% $</p> <p>Calculating the result gives:</p> <p>$ = 1.25\% $</p> <p>Thus, the fractional compression of water at this depth is 1.25%.</p>