Question

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 the mass of the earth to the mass of the moon is about

(a) 10

(b) 100

(c) 1000

(d) 10000

Answer 1

Correct option is (b) 100

The mass of the earth, \(M_e = \frac{gR_e^2}G\)

The mass of the moon, \(M_m = \frac{g'R_m^2}{G}\)

\(\therefore \frac{M_e}{M_m} = \frac{gR_e^2}{g'R_m^2}\)

\(= \frac{g}{\frac g6}\times \frac{R^2}{\left(\frac R4\right)^2}\)

⇒ \(\frac{M_e}{M_m} = 96\approx100\)