Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 36E / b / iii / Solution

Let $r_0=(3N{k}_{B}T/(4\pi P_0){)}^{1/3}$ be the zero-tension radius. From
$P_0{r}^3+2t{r}^2=P_0{r}_0^3$, put $r=r_0+\delta$ and retain first order:

Solved by gpt-5.6-sol high.