 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/36e/b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Let

r_{0} = (3 N k_{B} T / (4 π P_{0}))^{1/3}

be the zero-tension radius. From

P_{0} r^{3} + 2 t r^{2} = P_{0} r_{0}^{3}

, put

r = r_{0} + δ

and retain first order:

3 P_{0} r_{0}^{2} δ + 2 t r_{0}^{2} = 0, r = r_{0} - \frac{2 t}{3 P _{0}} + O (t^{2}) .

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