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

We need to find the fractional compression of water at a depth of 2.5 km below sea level.

The fractional change in volume due to pressure is given by:

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

where $$P$$ is the pressure at the depth and $$B$$ is the bulk modulus.

Calculate the pressure at depth $$h = 2.5 \, \text{km} = 2500 \, \text{m}$$:

$$P = \rho g h = 10^3 \times 10 \times 2500 = 2.5 \times 10^7 \, \text{N/m}^2$$

Calculate the fractional compression:

$$\frac{\Delta V}{V} = \frac{P}{B} = \frac{2.5 \times 10^7}{2 \times 10^9} = 1.25 \times 10^{-2} = 0.0125$$

Express as a percentage:

$$\frac{\Delta V}{V} = 0.0125 \times 100\% = 1.25\%$$

The correct answer is Option (1): 1.25%.