Question

When a large bubble rises from the bottom of a 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. 8 H
• B. 7 H
• C. 2 H
• D. H

Answer 1

Answer: (B)

7 H

Answer 2

Given : Initial radius of the bubble $=r$; Final radius of the bubble $=2 r$ and initial pressure at the surface $\left(P_{1}\right)=$ column of water height $H .$ When radius of a bubble becomes double, its volume $\left(V_{2}\right)$ becomes 8 times. Also from the Boyle's law, $P_{1} V_{1}=P_{2} V_{2}$ or $P_{2}=\frac{P_{1} V_{1}}{V_{2}}=\frac{H \times 8 V}{V}=8 H$ Therefore depth of the lake $=8 H-H=7 H$