Question

When a large bubble rises from the bottom of a lake to the surface. Its radius doubles. If atmospheric pressure is equal to that of column of water height H, then the depth of lake is

• A. H
• B. 2H
• C. 7H
• D. 8H

Answer 1

Answer: (C)

7H

Answer 2

$\left( P _ { 0 } + h \rho g \right) \times \frac { 4 } { 3 } \pi r ^ { 3 }$=$P _ { 0 } \times \frac { 4 } { 3 } \pi ( 2 r ) ^ { 3 }$

Where, h = depth of lake

⇒ $h \rho g = 7 P _ { 0 }$⇒ $h = 7 \times \frac { H \rho g } { \rho g } = 7 H$