MHT CET · Physics · Mechanical Properties of Fluids
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
- A H
- B 2 H
- C 7 H
- D 8 H
Answer & Solution
Correct Answer
(C) 7 H
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& P_1 V_1=P_2 V_2 \\
& \Rightarrow\left(P_0+h \rho g\right) \times \frac{4}{3} \pi r^3=P_0 \times \frac{4}{3} \pi(2 r)^3
\end{aligned}\)
Where, \(\mathrm{h}=\) depth of lake
\(\Rightarrow \mathrm{h} \rho \mathrm{~g}=7 \mathrm{P}_0 \Rightarrow \mathrm{~h}=7 \times \frac{\mathrm{H} \mathrm{\rho g}}{\rho g}=7 \mathrm{H}\)
& 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
\(\Rightarrow \mathrm{h} \rho \mathrm{~g}=7 \mathrm{P}_0 \Rightarrow \mathrm{~h}=7 \times \frac{\mathrm{H} \mathrm{\rho g}}{\rho g}=7 \mathrm{H}\)
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