Knowing that mass of Moon is `(M)/(81)` where M is the mass of Earth, find the distance at the distance at the point where gravitational 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 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 60 R)/(sqrt(M) + sqrt((M)/(81))) = (9)/(10) xx 60 R = 54 R` So , distance from the moon `= 60 R - 54R = 6 R`