Question

The mass of the moon is $\frac{1}{81}$ of the earth but the gravitational pull is $\frac{1}{6}$ of the earth. It is due to the fact that

• A. the radius of earth is $\frac{9}{\sqrt{6}}$ of the moon
• B. the radius of moon is $\frac{81}{6}$ of the earth
• C. moon is the satellite of the earth
• D. None of the above

Answer 1

Answer: (A)

Gravitational pull depends upon the acceleration due to gravity on that planet.
$M_m=\frac{1}{81}{M}_e,g_m=\frac{1}{6}{g}_e$
By the relation, $g=\frac{GM}{R^2}$
$\frac{R_e}{R_m}={\left(\frac{M_e}{M_m}\times \frac{g_m}{g_e}\right)}^{\frac{1}{2}}={\left(81\times \frac{1}{6}\right)}^{\frac{1}{2}}$
$\therefore$ $R_e=\frac{9}{\sqrt{69}}{R}_m$