JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Fluid Mechanics

For a soap bubble, the excess pressure is $\Delta P=\frac{4T}{r}$, where $T$ is surface tension. For the inner bubble (radius $r_1=3$ cm), the excess pressure with respect to the region between the bubbles is $\frac{4T}{3}$. The outer bubble (radius $r_2=6$ cm) contributes $\frac{4T}{6}=\frac{2T}{3}$ to the pressure inside. Total excess pressure inside the inner bubble with respect to atmospheric pressure: $P=\frac{4T}{3}+\frac{2T}{3}=2T$. For an equivalent single bubble with the same excess pressure: $\frac{4T}{r_{\text{eq}}}=2T$, giving $r_{\text{eq}}=2$ cm.