The mass of a planet is 2 times that of the earth and its diameter is twice that of the earth. If th

Question

The mass of a planet is 2 times that of the earth and its diameter is twice that of the earth. If the acceleration due to gravity on the earth is $9.8 \mathrm{~m/s}^2$, the acceleration due to gravity on that planet is

Professor PC Thomas Classes · Answer

(a) : The acceleration due to gravity is given by $g = \frac{GM}{R^2}$. For the earth, $g_E = \frac{GM_E}{R_E^2}$. For the planet, $M_P = 2M_E$ and $R_P = 2R_E$ (since diameter is doubled, radius is also doubled). Thus, $g_P = \frac{G(2M_E)}{(2R_E)^2} = \frac{2GM_E}{4R_E^2} = \frac{1}{2} \frac{GM_E}{R_E^2} = \frac{g_E}{2}$. Given $g_E = 9.8 \mathrm{~m/s}^2$, we get $g_P = \frac{9.8}{2} = 4.9 \mathrm{~m/s}^2$.