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Two soap bubbles are stuck together with...

Two soap bubbles are stuck together with an intermediate film separating them. Compute the radius of curvature of this film given that the radii of the bubbles in this arrangement are `r_(1)` and `r_(2)` respectively. If `r_(1) gt r_(2)` state clearly which way the intermediate film will bulge.
For the case when `r_(1)=r_(2)=2cm` calculate he radius of the bubble formed by bursting the intermediate film. The volume of a spherical dome of radius `R` and height `h` is `pib^(2)(3R-b)//3`.

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