If average depth of an ocean is 4000 m and the bulk modulus of water is 2 × 10⁹ N m⁻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 m s⁻², ρ = 1000 kg m⁻³) Numerical answer type. Work it out, then open the answer.

Answer: 2. Pressure at the bottom: P = ρ g h = 1000 × 10 × 4000 = 4 × 10⁷ Pa. (Δ V)/(V) = P/B = 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)

Q11JEE Main 2024 · 27 JAN · SHIFT 1Medium

Density, Compressibility & Pascal's Law

If average depth of an ocean is $4000\text{ m}$ and the bulk modulus of water is $2 \times 10^{9}\text{ N m}^{-2}$ , 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, $g = 10\text{ m s}^{-2},\ \rho = 1000\text{ kg m}^{-3}$ )

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

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Answer: 2

Pressure at the bottom: $P = \rho g h = 1000 \times 10 \times 4000 = 4 \times 10^{7}$ Pa.
$\dfrac{\Delta V}{V} = \dfrac{P}{B} = \dfrac{4 \times 10^{7}}{2 \times 10^{9}} = 2 \times 10^{-2}$
So $\alpha = 2$ .

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