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?

Options

A. `(D)/(2)`
B. `(2D)/(3)`
C. `(4D)/(5)`
D. `(9D)/(10)`

Answer

D

Explanation

At `P:g=(GM)/(x^(2))-(G81M)/((D-x)^(2))=0`
`impliesD-x=9x,10x=D`
`x=(D)/(10)` from the moon and `(9D)/(10)` from the earth