Question

An air bubble of radius r rises from the bottom of a tube of depth H. When it reaches the surface, its radius becomes 3r. What is the atmospheric pressure in terms of height of water column?

• A. $\frac{H}{2}$
• B. $\frac{H}{4}$
• C. $\frac{H}{8}$
• D. $\frac{H}{26}$

Answer 1

The correct option is D $\frac{H}{26}$

$P_1{V}_1=P_2{V}_2$
$\Rightarrow (P_o+H\rho g)\frac{4}{3}\pi r^3=P_o\frac{4}{3}\pi (3r{)}^3$
$\Rightarrow P_o+H\rho g=27P_o$
$\Rightarrow P_o=\frac{H}{26}\rho g$