Four spheres, each of mass m, are placed at the corners of a square of side d. A fifth sphere of mass M is placed at the centre of the square. What is the total gravitational potential energy of the system?

- Gm/d [(4 + sqrt(2))m + 4*sqrt(2)*M]
- Gm/d [(4 + sqrt(2))*M + 4*sqrt(2)*m]
- Gm/d [3m² + 4*sqrt(2)*M]
- Gm/d [6m² + 4*sqrt(2)*M]

Correct answer: - Gm/d [(4 + sqrt(2))m + 4*sqrt(2)*M]

Solution

There are 4 adjacent m-m pairs (distance d), 2 diagonal m-m pairs (distance d*sqrt(2)), and 4 m-M pairs (distance d/sqrt(2)). Summing all pair PE gives the total.

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