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

(c ) `(g_(M))/(g_(E))=((G(M_(E)//8))/(R_(M)^(2)))/((GM_(E))/(R_(E)^(2)))=(R_(E)^(2))/(8R_(M)^(2))`.......(i)
where the subscript M and E are for the moon and the earth respectively.
Given, `(g_(M))/(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)`