Question

$R$ and $r$ are the radii of the Earth and the Moon respectively and ${\rho }_e$ 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. $\frac{R}{r}\cdot \frac{{\rho }_e}{{\rho }_m}$
• B. $\frac{r}{R}\cdot \frac{{\rho }_e}{{\rho }_m}$
• C. $\frac{r}{R}\cdot \frac{{\rho }_m}{{\rho }_e}$
• D. $\frac{R}{r}\cdot \frac{{\rho }_m}{{\rho }_e}$

Answer 1

The correct option is A $\frac{R}{r}\cdot \frac{{\rho }_e}{{\rho }_m}$

Acceleration due to gravity $=g=Gm/r^2$

Also, mass $=m=\rho V$

$\Rightarrow m_e={\rho }_e\times \frac{4}{3}\pi R^3$

$\Rightarrow m_m={\rho }_m\times \frac{4}{3}\pi r^3$

$\Rightarrow \frac{g_e}{g_m}=\frac{G{m}_e/R^2}{G{m}_m/r^2}=\frac{{\rho }_{e}R}{{\rho }_{m}r}$

Hence correct answer is option $A$