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. The radius of the moon is `81/6` of the earth
B. The radius of the earth is `9/(sqrt(6))` of the moon
C. Moon is the satellite of the earth
D. none of these

Answer

B

Explanation

Gravitational pull depends upon the acceleration due to gravity on that planet.
`:. M_(m)=1/81 M_(e), g_(m)=1/6 g_(e)`
`g=(Gm)/(R^(2)) implies (R_(e))/(R_(m))=((M_(e))/(M_(m))xx(g_(m))/(g_(e)))^(1//2)=(81xx1/6)^(1//2)`
`:. R_(e)=9/(sqrt(6))R_(m)`