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Question

Mass of the earth is 81 times the mass of the moon and distance between the earth and moon is 60 times the radius of the earth. If R is radius of the earth, then the distance between moon and the point on the line joining the moon and the earth where the gravitation force becomes zero is

A

30R

B

15R

C

6R

D

5R

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Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is C)

Let m be the mass at a distance x from the centre of the moon where gravitational force is zero.
$∴ \frac{G M _{e} m}{( 6 0 R - x ) ^{2}} = \frac{G M _{m o o n} m}{x ^{2}} o r \frac{8 1}{( 6 0 R - x ) ^{2}} = \frac{1}{x ^{2}} o r \frac{9}{6 0 R - x} = \frac{1}{x} o r x = 6 R$

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