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Asked in JEE Main 17th March 1st Shift 2021 · Two bubbles and common surfaces
Given: two soap bubbles of radii a and b with b>a, sharing a common film after coalescing.
With the outside at p₀, the interiors are at pₐ=p₀+(4T)/a and p_b=p₀+(4T)/b, so the smaller bubble holds the higher pressure.
The common surface is itself a soap film with two surfaces, bulging into the larger bubble, and it must support pₐ-p_b=(4T)/r.
(4T)/r=4T(1/a-1/b), so 1/r=(b-a)/(ab).
r=(ab)/(b-a).
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