Question

A glass tube of uniform internal radius `(r)` has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End `1` has a hemispherical soap bubble of radius `r`. End `2` has sub-hemispherical soap bubble as shown in figure. Just after opening the valve.

A. air from end 1 flows towards end 2. No change in the volume of the soap bubbles
B. air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decrease
C. no change occurs
D. air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increase

Answer 1

Correct Answer - B
Excess pressure across a bubble is inversely proportional to the raius of the bubble, i.e. `Deltap prop (1)/(r )`
Since the value of r of the sub-hemispherical bubble is more than that for a hemispherical bubble, the exces pressue across the bubble at end 2 is less than that atend 1. Hence air from end 1 will flow towards end 2 resulting in a decrease in the volume of the bubble at end 1. Thus the correct choice is B.