Question

Prove that if two bubbles of radii `r_(1)` and `r_(2)(r_(1)ltr_(2))` come in contact with each other then the radius of curvature of the common surface `r=(r_(1)r_(2))/(r_(2)-r_(1))`

Answer 1

`becauser_(1)ltr_(2)thereforeP_(1)gtP_(2)` small part of bubbles is in equilibrium
`impliesP_(1)(DeltaA)-P_(2)(DeltaA)=(4T)/(r)DeltaAimplies(4T)/(r_(1))-(4T)/(r_(2))=(4T)/(r)impliesr=(r_(1)r_(2))/(t_(2)-t_(1))``