Question

An air bubble doubles in radius on rising from the bottom of a lake to its surface. If the atmospheric pressure is equal to that of a column of water of height H, the depth of lake is

(a) H 

(b) 2H

(c) 7H 

(d) 8H

Answer 1

(c) 7H 

 Since the radius becomes double, the volume becomes eight times. Therefore, according to Boyle’s law, the pressure becomes one-eighth. Now, the pressure at the surface Hρg. Therefore pressure at the bottom must be 8 Hρg. Hence the depth of the lake is 7H.