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Two identical particles, of total combined mass M, are placed a certain distance apart in empty space and released. The only force between them is their mutual gravitational attraction, with no external force. When their separation is R, the magnitude of the acceleration of one particle relative to the other is

1. G*M/(2*R²)
2. G*M/R²
3. 2*G*M/R²
4. cannot be found from the information given

Correct answer: G*M/R²

Solution

Each particle has mass M/2. The gravitational force between them is G*(M/2)*(M/2)/R². Each particle's acceleration is force divided by its own mass M/2. Since they accelerate toward each other, the relative acceleration is the sum of the two accelerations.

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