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 $=2 \times 10^{9} \mathrm{Nm}^{-2}$, density of water $=10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$, acceleration due to gravity $=\mathrm{g}=10 \mathrm{~ms}^{-2}$.

JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Fluid Mechanics

The fractional compression

(\frac{Δ V}{V})

of water at the depth of 2.5 km below the sea level is

____

%. Given, the Bulk modulus of water

= 2 \times 1 0^{9} Nm^{- 2}

, density of water

= 1 0^{3} kg m^{- 3}

, acceleration due to gravity

= g = 10 ms^{- 2}

(A)1.75
(B)1.0
(C)1.5
(D)1.25✓ Correct

Answer: (D)

Solution

At depth

h

, the increase in pressure is

Δ P = ρ g h = 1 0^{3} \times 10 \times 2.5 \times 1 0^{3} = 2.5 \times 1 0^{7} Pa

Bulk modulus relates pressure change to fractional volume change:

B = \frac{Δ P}{Δ V / V} ⟹ \frac{Δ V}{V} = \frac{Δ P}{B} = \frac{2.5 \times 1 0 ^{7}}{2 \times 1 0 ^{9}} = 1.25 \times 1 0^{- 2}

As a percentage, the fractional compression is 1.25%.

JEE Main · 2025 · 29 Jan 2025 · Shift 1 · Single correct option

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