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)

$R_m=\frac{1}{4}{R}_E{g}_m=\frac{1}{5}{g}_{E}g=\frac{GM}{R^2}\therefore \frac{g_E}{g_m}=\frac{\frac{G{M}_E}{{R_E}^2}}{\frac{G{M}_m}{{R_m}^2}}=\frac{M_E}{M_m}.{\left(\frac{R_m}{R_E}\right)}^2\therefore \frac{M_E}{M_m}=\left(\frac{g_E}{g_m}\right){\left(\frac{R_m}{R_E}\right)}^2\Rightarrow 5\times 4^2=\frac{80}{1}\Rightarrow M_E:M_m=80:1$