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Sagot :
The gravitational force F between two masses M and m a distance r apart is
F = G M m / r ²
Decrease the distance by a factor of 7 by replacing r with r / 7, and decrease both masses by a factor of 8 by replacing M and m with M / 8 and m / 8, respectively. Then the new force F* is
F* = G (M / 8) (m / 8) / (r / 7)²
F* = (1/64 × G M m) / (1/49 × r ²)
F* = 49/64 × G M m / r ²
In other words, the new force is scaled down by a factor of 49/64 ≈ 0.7656, so the new force has magnitude approx. 76.56 N.
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