**1. The problem statement, all variables and given/known data**

Two bubbles, one of radius R and the other of radius 3R come into contact with each other. What is the distance between the centres of the two bubbles? Ignore the weight of the bubbles.

**2. Relevant equations**

p(inside bubble)= p(atm) + 4T/R where T is the surface tension and R the radius of the bubble

**3. The attempt at a solution**

The radius of the common surface of the bubbles comes out to be 3R/2. I’ve taken the radius of the circle that is common to both bubbles as r. Now I’ve balanced the forces first on this common surface which gave me:

(2r)/(3R) = sin theta where theta is the semi vertical angle of the cone subtended by this common surface onto the centre of the imaginary sphere of which the common surface is a part of.

Then I balanced forces on the surfaces of the two bubbles which gave me:

r/R = sin alpha where alpha is the semi-vertical angle of the cone subtended by the common surface onto the centre of the smaller bubble.

r/(3R) = sin beta where beta is the semi-vertical angle of the cone subtended by the common surface onto the centre of the larger bubble.

I don’t know what to do next. I have a feeling that the question is missing some information.

http://ift.tt/1g2Q6Ga