Q122 / 150 · MHT CET 2024 (09 May Shift 1) · Physics
When an air bubble rises from the bottom of lake to the surface, its radius is doubled. The atmospheric pressure is equal to that of a column of water of height ' $H$ '. The depth of the lake is
- AH
- B2 H
- Correct answerC7 H
- D8 H
Solution
$\begin{aligned}
& P_1 V_1=P_2 V_2 \\
& \Rightarrow\left(P_0+h \rho g\right) \times \frac{4}{3} \pi r^3=P_0 \times \frac{4}{3} \pi(2 r)^3
\end{aligned}$
Where, $\mathrm{h}=$ depth of lake $\Rightarrow \mathrm{h} \rho \mathrm{~g}=7 \mathrm{P}_0 \Rightarrow \mathrm{~h}=7 \times \frac{\mathrm{H} \mathrm{\rho g}}{\rho g}=7 \mathrm{H}$
Where, $\mathrm{h}=$ depth of lake $\Rightarrow \mathrm{h} \rho \mathrm{~g}=7 \mathrm{P}_0 \Rightarrow \mathrm{~h}=7 \times \frac{\mathrm{H} \mathrm{\rho g}}{\rho g}=7 \mathrm{H}$
Hence, the correct answer is option: 'C'.