 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-4/9b/a/solution

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

For

I = \frac{1}{2} \sum m_{i} ∣ x_{i} ∣^{2}

, differentiation gives

\ddot{I} = 2 T + \sum_{i} x_{i} \cdot F_{i} = 2 T + V,

because the Newtonian potential is homogeneous of degree

- 1

. Bounded positions and velocities imply

\overline{\ddot{I}} = 0

, so the virial theorem gives

\overline{T} = - \overline{V} /2

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