If acceleration due to gravity on the surface of moon is `(1//5)^("th")` that at the surface of the earth and radius of the moon is `(1//4)^("th")` that of the earth, then the ratio of the mass of the earth to mass of moon is

Options

A. 20
B. 40
C. 60
D. 80

Answer

d

Explanation

On the earth,
`g=(GM)/(r^(2))" "therefore M=(gR^(2))/(G)`
On the moon,
`(g)/(5)=(GM')/((R//4)^(2)) therefore M'(gR^(2))/(80G)=(M)/(80)`
`(M)/(M')=80`