If average depth of an ocean is 4000 m and the bulk modulus of water is 2 × 10 9 Nm -2 , then fractional compression frac 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 )

Physics · Fluid Mechanics

JEE Main 2024 — 27 January, Shift 1 — Question 57

If average depth of an ocean is 4000 m and the bulk modulus of water is $2 \times 10^{9} \mathrm{Nm}^{-2}$ , then fractional compression $\frac{\Delta \mathrm{V}}{\mathrm{V}}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$ . The value of $\alpha$ is $\qquad$

(Given, $\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ )

Answer: 2

Numerical answer — enter this value.

Step-by-step solution

$\mathrm{B}=-\frac{\Delta \mathrm{P}}{\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)}$

$-\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)=\frac{\rho \mathrm{gh}}{\mathrm{B}}=\frac{1000 \times 10 \times 4000}{2 \times 10^{9}}$

$=2 \times 10^{-2}[-\mathrm{ve}$ sign represent compression]

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 27 January, Shift 1
Subject: Physics
Chapter: Fluid Mechanics
Topic: Properties of Fluids & Hydrostatic Pressure