The fractional compression ( \frac\Delta VV ) of water at the depth of 2.5 km below the sea level is \underline\hspace2cm %. 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 .

Properties of Matter PYQ — JEE Main 2025 · 29 Jan · Shift 1 · Q56 with Solution

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Correct answer: B

At a depth $h = 2.5\,\text{km} = 2500\,\text{m}$ below sea level, the excess pressure due to water is

P = \rho g h

Given:

\rho = 10^3\,\text{kg m}^{-3},\quad g = 10\,\text{m s}^{-2},\quad h = 2500\,\text{m}

So,

P = 10^3 \times 10 \times 2500 = 2.5 \times 10^7\,\text{Pa}

Bulk modulus is defined as

B = -\frac{\Delta P}{\Delta V/V}

Hence, the magnitude of fractional compression is

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

Given:

B = 2 \times 10^9\,\text{Pa}

Therefore,

\frac{\Delta V}{V} = \frac{2.5 \times 10^7}{2 \times 10^9}

= 1.25 \times 10^{-2}

1.25 \times 10^{-2} = 0.0125

In percent,

0.0125 \times 100 = 1.25\%

So the correct option is:

\boxed{\text{B } (1.25\%)}