The radius of the Moon is about one-fourth that of the Earth and acceleration due to gravity on the Moon is about one-sixth that on the Earth From this, we can conclude that the ratio of mass of Earth to the mass of the Moon is about

Options

A. 10
B. 100
C. 1000
D. 10000

Answer

B

Explanation

`R_m=R_e//4 , g_m=g_e//6`
`g=GM//R_2`
`g_e//g_m=(M_e//R_e^2)//(M_m//R_m)^2`
`g_e//g_m=(M_e//M_m)//(R_m//R_e)^2`
`(M_e//M_m)=(g_e//g_m)X(R_e//R_m)^2=(6g_m//g_m)X (4R_m//R_m)^2`
`=6xx4xx4=96~~100`