The radius of the Moon is frac{1}{4} times th | vedclass

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(B) The acceleration due to gravity on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M

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$\frac{g}{5}$

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(B) The acceleration due to gravity on the surface of a planet is given by the formula $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mass of the planet,and $R$ is its radius.For Earth: $g_e = \frac{GM_e}{R_e^2}$.For the Moon: $g_m = \frac{GM_m}{R_m^2}$.Given that $M_m = \frac{M_e}{80}$ and $R_m = \frac{R_e}{4}$.Taking the ratio of the two accelerations:$\frac{g_m}{g_e} = \frac{M_m}{M_e} 	imes \left( \frac{R_e}{R_m} ight)^2$Substituting the given values:$\frac{g_m}{g_e} = \left( \frac{1}{80} ight) 	imes \left( \frac{4}{1} ight)^2 = \frac{1}{80} 	imes 16 = \frac{16}{80} = \frac{1}{5}$.Therefore,$g_m = \frac{g_e}{5} = \frac{g}{5}$.

The radius of the Moon is $\frac{1}{4}$ times that of the Earth,and its mass is $\frac{1}{80}$ times that of the Earth. If the acceleration due to gravity on Earth is $g$,what is the acceleration due to gravity on the Moon?

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