The mass of the moon is ` (1)/(8)` of the earth but the gravitational pull is ` (1)/(6)` earth It is due to the fact that .

Options

A. moon is the satelite of the earth
B. the radius of the earth is `8//6` of the moon radius
C. the radius of the earth is `sqrt(8//6)` of the moon radius
D. the radius of the moon is `6//8` of the earth radius

Answer

C

Explanation

As `(G_(m))/(G_(e ))=G(M//8R_(m)^(2))/(GM//R_(e )^(2))=(R_(e )^(2))/(8R_(m)^(2))`
Given `(mg_(m))/(mg_(e ))=1/6 rarr (g_(m))/(g_(e ))=1/6`
From Eqs I and ii we get
`(R_(e )^(2))/(8R_(m)^(2))=1/6` or `R_(e )=R_(m)sqrt(8)/(6)`