Excess Pressure: Drops & Bubbles question from MHT CET 2023 (14 May, Shift 2)

Answer: (c)

1. Isothermal, pressure terms from surface tension only (vacuum / neglect outside pressure): $PV$ is conserved.
2. For a soap bubble $P = \frac{4T}{r}$, so $PV = \frac{4T}{r} \cdot \frac{4}{3}\pi r^3 \propto r^2$.
3. $\frac{4T}{R}R^3 = \frac{4T}{a}a^3 + \frac{4T}{b}b^3 \Rightarrow R^2 = a^2 + b^2$
4. So the answer is (c) $\sqrt{a^2 + b^2}$.