If average depth of an ocean is 4000 m and the bulk modulus of water is 2 × 10⁹ Nm⁻², then fractional compression (Δ V)/(V) of water at the bottom of ocean is α × 10⁻². The value of α is _______ (Given, g = 10 ms⁻², ρ = 1000 kg m⁻³) Numerical answer type. Work it out, then open the answer.

Answer: 2. (Δ V)/(V) = (ρ g h)/(B) ρ g h = 1000×10×4000 = 4×10⁷ Pa (Δ V)/(V) = 4×10⁷2×10⁹ = 2×10⁻², so α = 2.

If average depth of an ocean is 4000 m and the bulk modulus of water… | JEE Main 2024 (27 Jan, Shift 1)

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Bulk Modulus & Compressibility

If average depth of an ocean is $4000\text{ m}$ and the bulk modulus of water is $2 \times 10^{9}\text{ Nm}^{-2}$ , then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$ . The value of $\alpha$ is _______ (Given, $\text{g} = 10\text{ ms}^{-2},\ \rho = 1000\text{ kg m}^{-3}$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 2

$\frac{\Delta V}{V} = \frac{\rho g h}{B}$
$\rho g h = 1000\times10\times4000 = 4\times10^{7}\ \text{Pa}$
$\frac{\Delta V}{V} = \frac{4\times10^{7}}{2\times10^{9}} = 2\times10^{-2}$ , so $\alpha = 2$ .

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