The distance of the centres of moon the earth is D. The mass of earth is 81 times the mass of the moon. At what distance from the centre of the earth, the gravitational force on a particle will be zero.

Options

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

Answer

d

Explanation

`(GM_(e))/(x^(2))=G(M_(m))/((D-x)^(2))" "therefore(81)/(x^(2))=(1)/((D-x)^(2))`
`therefore 9(D-x)=x" "therefore x=(9D)/(10)`