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Question

The point at which the gravitational force acting on any mass is zero due to the Earth and the Moon system is (The mass of the Earth is approximately 81 times the mass of the Moon and the distance between the Earth and the Moon is 3,85,000km.)

A
36,000 km from the Moon.
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B
38,500 km from the Moon.
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C
34500 km from the Moon.
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D
30,000 km from the Moon.
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Solution

The correct option is D 38,500 km from the Moon.
For zero gravitational force acting on the mass m1,
GMm1(dx)2=Gmm1x2
Here x is distance from moon, M is mass of earth, m is mass of moon and d is the distance between the earth and moon.
M(dx)2=mx2
81m(dx)2=mx2
81(dx)2=1x2
(dx)281=x2
dx9=x
Solving gives: x=d10=38,500 km

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