JEE MAIN - Physics (2024 - 27th January Morning Shift - No. 30)
If average depth of an ocean is $$4000 \mathrm{~m}$$ and the bulk modulus of water is $$2 \times 10^9 \mathrm{~Nm}^{-2}$$, 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, $$\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$$)
Answer
2
Explanation
$$\begin{aligned}
& \mathrm{B}=-\frac{\Delta \mathrm{P}}{\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)} \\
& -\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)=\frac{\rho \mathrm{gh}}{\mathrm{B}}=\frac{1000 \times 10 \times 4000}{2 \times 10^9} \\
& =2 \times 10^{-2}[-\mathrm{ve} \text { sign represent compression }]
\end{aligned}$$
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