Excess Pressure: Drops & Bubbles question from JEE Main 2021 (17 Mar, Shift 1)

Answer: (d)

1. The smaller bubble ($a$) has higher pressure, so the common film bulges into the bigger one.
2. Pressure difference across the film: $\frac{4T}{r} = \frac{4T}{a} - \frac{4T}{b}$
3. $\frac{1}{r} = \frac{b-a}{ab} \Rightarrow r = \frac{ab}{b-a}$
4. So the answer is (d) $\frac{ab}{b-a}$.