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

Answer

C

Explanation

`(gM)/(g_(E))=((G(M_(E)//8))/(R_(E)^(2)))/((GM_(E))/(R_(E)^(2)))=(R_(E)^(2))/(8R_(M)^(2))..........(i)`
Where the subcipts M and E are for the moon and the earth respectively.
Given, `(gM)/(g_(E))=1/6........(ii)`
From (i) and (ii), we get
`(R_(E)^(2))/(8R_(M)^(2))=1/6` or `R_(E)=sqrt(8/6)R_(M)`