Q 11-08-039JEE MainJEE Main 2024 (27 Jan, Shift 1)Easy
If average depth of an ocean is $4000\ \text{m}$ and the bulk modulus of water is $2\times10^9\ \text{N m}^{-2}$, then fractional compression $\dfrac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha\times10^{-2}$. The value of $\alpha$ is ______. (Given, $g = 10\ \text{m s}^{-2}$, $\rho = 1000\ \text{kg m}^{-3}$)
Numerical value type. Enter your answer.
Answer: 2
Extra pressure at the bottom: $\Delta P = \rho g h = 1000\times10\times4000 = 4\times10^7\ \text{Pa}$
$$\frac{\Delta V}{V} = \frac{\Delta P}{B} = \frac{4\times10^7}{2\times10^9} = 2\times10^{-2} \;\Rightarrow\; \alpha = 2$$
Solution by Sreeraj P, M.Sc Physics