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

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

Q6JEE Main 2025 · 29 JAN · SHIFT 1Medium

Bulk Modulus & Compressibility

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)

$\frac{\Delta V}{V} = \frac{\rho g h}{B}$
$\rho g h = 10^{3}\times10\times2500 = 2.5\times10^{7}\ \text{Pa}$
$\frac{\Delta V}{V} = \frac{2.5\times10^{7}}{2\times10^{9}} = 1.25\times10^{-2} = 1.25\%$
So the answer is (b).

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Bulk Modulus & Compressibility question from JEE Main 2025 (29 Jan, Shift 1)

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