 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/9d/b/solution

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

ij

and

ji

terms and use

f_{ji} = - f_{ij}

\sum_{i} F_{i} \cdot r_{i} = \sum_{i} \sum_{j < i} f_{ij} \cdot (r_{i} - r_{j}) .

f_{ij} = - G m^{2} (r_{i} - r_{j}) /∣ r_{i} - r_{j} ∣^{3}

, so each summand is

- G m^{2} /∣ r_{i} - r_{j} ∣

. Their sum is

V

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