Question

The mass and radius of a planet are half the respective values of the earth. What is the value of
acceleration due to gravity of the planet?

Answer 1

M'=M/2. R'=R/2 g'=GM'/R'²=GM/2R'²=GM/2×R²/4=4GM/2R²=2(GM/R²).....g'=2g ...g'=19.6 m/s²

Answer 2

$let\ mass\ of\ earth=M_e\\radius\ of\ earth=r_e\\acceleration\ due\ to\ gravity=g_e\\ \\let\ mass\ of\ planet=M_p= \frac{M_e}{2}\\ thus \frac{M_p}{M_e}=\frac{1}{2}\\radius\ of\ planet=r_p= \frac{r_e}{2}\\ thus\ \frac{r_e}{r_p} =2\\acceleration\ due\ to\ gravity=g_p\\ \\ \frac{g_p}{g_e} = \frac{GM_p}{ (r_p)^{2} } /\frac{GM_e}{ (r_e)^{2} }\\ \\ \frac{g_p}{g_e} = \frac{GM_p}{ (r_p)^{2} } *\frac{ (r_e)^{2} }{GM_e}= \frac{M_p}{M_e}* (\frac{r_e}{r_p}) ^2 = \frac{1}{2}*4=2 \\ \\ g_p=2*g_e=2*9.81=\boxed{19.62\ m/s^2}$