JEE MAIN - Physics (2025 - 29th January Morning Shift - No. 6)
The fractional compression $\left( \frac{\Delta V}{V} \right)$ of water at the depth of 2.5 km below the sea level is __________ %. Given, the Bulk modulus of water = $2 \times 10^9$ N m$^{-2}$, density of water = $10^3$ kg m$^{-3}$, acceleration due to gravity $g = 10$ m s$^{-2}$.
1.0
1.25
1.75
1.5
Explanation
$$\begin{aligned}
& \mathrm{B}=\frac{\rho \mathrm{gh}}{\left(\frac{\Delta \mathrm{v}}{\mathrm{v}}\right)} \\
& \frac{\Delta \mathrm{v}}{\mathrm{v}} \times 100=\frac{\rho \mathrm{gh}}{\mathrm{~B}} \times 100 \\
& \frac{1000 \times 10 \times 2.5 \times 10^3}{2 \times 10^9} \times 100 \% \\
& =1.25 \%
\end{aligned}$$
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