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The distance between the centres of the Earth and the Moon is D, and the Earth's mass is 81 times the Moon's. At what distance from the Earth's centre is the net gravitational field zero?

1. D/2
2. 2D/3
3. 4D/5
4. 9D/10

Correct answer: 9D/10

Solution

Let the null point be at distance x from Earth's centre. Set M_E/x² = M_M/(D-x)² with M_E = 81 M_M: 81/x² = 1/(D-x)² => 9/x = 1/(D-x) => 9(D - x) = x => 9D = 10x => x = 9D/10.

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