The fractional compression ((Δ V)/(V)) of water at the depth of 2.5 km below the sea level is __________ %. Given, the Bulk modulus of water = 2 × 10⁹ N m ⁻², density of water = 10³ kg m ⁻³, acceleration due to gravity g = 10 m s ⁻². (a) 1.0 (b) 1.25 (c) 1.75 (d) 1.5

Answer: (b). Extra pressure at depth h: P = ρ g h = 10³ × 10 × 2500 = 2.5 × 10⁷ Pa. (Δ V)/(V) = P/B = 2.5 × 10⁷2 × 10⁹ = 1.25 × 10⁻² So the answer is (b) 1.25%.

The fractional compression ((Δ V)/(V)) of water at the depth of 2.5… | JEE Main 2025 (29 Jan, Shift 1)

Q8JEE Main 2025 · 29 JAN · SHIFT 1Medium

Density, Compressibility & Pascal's Law

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 $^{-2}$ .

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Answer: (b)

Extra pressure at depth $h$ : $P = \rho g h = 10^{3} \times 10 \times 2500 = 2.5 \times 10^{7}$ Pa.
$\dfrac{\Delta V}{V} = \dfrac{P}{B} = \dfrac{2.5 \times 10^{7}}{2 \times 10^{9}} = 1.25 \times 10^{-2}$
So the answer is (b) $1.25\%$ .

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