Question

The radius and acceleration due to gravity of the moon are $\frac{1}{4}$ and $\frac{1}{5}$ that of the earth, the ratio of the mass of the earth to mass of the moon is :

• A. $1:80$
• B. $80:1$
• C. $1:20$
• D. $20:1$

Answer 1

Answer: (B)

$80:1$

Given that:

$\frac{g_m}{g_e}=\frac{1}{5}and\frac{R_m}{R_e}=\frac{1}{4}\frac{g_m}{g_e}=\frac{G\times M_m\times R_e^2}{R_m^2\times G\times M_e}=>\frac{1}{5}=\frac{M_m}{M_e}\times {\left(\frac{R_e}{R_m}\right)}^2=>\frac{1}{5}=\frac{M_m}{M_e}\times 16=>\frac{M_e}{M_m}=\frac{80}{1}$