The mass of a planet is $\frac{1}{10}$ th that of the earth and its diameter is half that of the ear

Question

The mass of a planet is $\frac{1}{10}$ th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is

Professor PC Thomas Classes · Answer

(d) : Given, $M_P=\frac{M_E}{10}$ and $D_P=\frac{D_E}{2}$ or $R_P=\frac{R_E}{2}$ As, $g_E=\frac{G M_E}{R_E^2}$ $ g_p=\frac{G M_P}{R_P^2} \ $ from equation (i) and (ii) $ \frac{g_P}{g_E}=\frac{M_P}{R_P^2} 	imes \frac{R_E^2}{M_E}=\left(\frac{M_E}{10}ight) 	imes\left(\frac{4}{R_E^2}ight) 	imes \frac{R_E^2}{M_E} $ $	herefore g_p=\frac{2}{5} g_E \Rightarrow g_P=\frac{2}{5} 	imes 9.8=3.92 \mathrm{~m} \mathrm{~s}^{-2}$