The distance between the centres of the Moon and the earth is D. The mass of the earth is 81 times the mass of the Moon. At what distance from the centre of the Earth, the gravitational force will be zero?

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The distance between the centres of the Moon and the earth is D. The mass of the earth is 81 times the mass of the Moon. At what distance from the centre of the Earth, the gravitational force will be zero?

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$\frac{D}{2}$

$\frac{2 D}{3}$

$\frac{4 D}{3}$

$\frac{9 D}{10}$

answer is D.

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Detailed Solution

$\begin{array}{l} \frac{81 GM}{x^{2}} = \frac{GM}{(D - x)^{2}} \\ \Rightarrow \frac{9}{x} = \frac{1}{(D - x)} \\ \Rightarrow x = \frac{9}{10} D \end{array}$