Knowing that mass of Moon is `(M)/(81)` where Mis the mass of Earth, find the distance at the point where gravitation
field due to Earth and Moon cancel each other, from the Moon. Given that distance between Earth and Moon
is 60 R. Where R is the radius of Earth.

Options

A. 2 R
B. 4 R
C. 6 R
D. 8 R

Answer

C

Explanation

Point of zero intensity `"x"=(sqrt(m_(1))d)/(sqrt(m_(1))+sqrt(m_(2)))`
Mass of the earth `m_(1)=M,` Mass of the moon `m_(2)=(M)/(81)`
and distance between earth and moon d= 60 R
Point of zero intensity from the earth
`"x"=(sqrt(M) xx 60R)/(sqrt(M)+sqrt((M)/(81)))=(9)/(10)xx 60 R= 54 R`
So distance from the moon = 60 R- 54 R=6R