The distance between the centres of the Earth and Moon is D. The mass of the Earth is 81 times the mass of the Moon. At what distance from the centre of the Earth is the net gravitational force on a test mass zero?
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Question

The distance between the centres of the Earth and Moon is D. The mass of the Earth is 81 times the mass of the Moon. At what distance from the centre of the Earth is the net gravitational force on a test mass zero?

Options

G1 Physics · Accepted Answer

Let the zero-field point be at distance x from Earth's centre. Then its distance from the Moon is D-x. Equating field magnitudes: GMₑ/x² = GMₘ/(D-x)². Since Mₑ = 81Mₘ, 9/x = 1/(D-x). Hence 9(D-x)=x, so x = 9D/10. Correct answer: D.