question_answer

R and r are the radii of the Earth and Moon respectively. \[{{\rho }_{e}}\]and\[{{\rho }_{m}}\]are the densities of the Earth and Moon respectively. The ratio of acceleration due to gravity on the surface of the Earth to the Moon is (a) \[\frac{R}{r}.\frac{{{\rho }_{e}}}{{{\rho }_{m}}}\]                        (b) \[\frac{r}{R}.\frac{{{\rho }_{e}}}{{{\rho }_{m}}}\] (c) \[\frac{r}{R}.\frac{{{\rho }_{m}}}{{{\rho }_{e}}}\]                        (d) \[\frac{R}{r}.\frac{{{\rho }_{m}}}{{{\rho }_{e}}}\]

Answer:

Earth	Moon
\[{{R}_{e}}=R\]	\[{{R}_{m}}=r\]
\[{{d}_{e}}={{\rho }_{e}}\]	\[{{d}_{m}}={{\rho }_{m}}\]

\[\frac{{{g}_{e}}}{{{g}_{m}}}=?\] \[g=\frac{4}{3}\pi GdR\]                               \[\Rightarrow \] \[g\propto dR\]                              (\[\because \]G constant)