Q. The mass of the moon is 1/8 of the earth but the gravitational pull is 1/6 of the earth. It is due to the fact that
A) Moon is the satellite of the earth
B) The radius of the earth is 8.6 the moon
C) The radius of the earth is $\sqrt{8/6}$ of the moon
D) The radius of the moon is 6/8 of the earth
Explanation
(c) $\frac{g_{m}}{g_{e}} = \frac{G(M/8)}{GM/R_{e}^{2}} = \frac{R_{e}^{2}}{8R_{m}^{2}};\ \ldots(i)$
Given, $\frac{mg_{m}}{mg_{e}} = \frac{1}{6}$
or $\frac{g_{m}}{g_{e}} = \frac{1}{6}$ …(ii)
From Eqs. (i) and (ii); $\frac{R_{e}^{2}}{8R_{m}^{2}} = \frac{1}{6}$
or $R_{e} = \sqrt{8/6}R_{m}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.