Surface tension question.

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.

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