Question

What will be the acceleration due to gravity on the surface of the moon, if its radius is1/4 the radius of the Earth and its mass is 1/80 times the mass of the Earth? (Take g as 9.8 m/s²)

Answer 1

Let earth's radius = $R_e$
Earth's mass =  $M_e$

moon's radius = $R_m=\frac{R_e}{4}$
Earth's mass =  $M_m=\frac{M_e}{80}$

$g_e = \frac{GM_e}{R_e^2}$ = 9.8 ms²

$g_m= \frac{GM_m}{R_m^2} = \frac{G(M_e/80)}{(R_e/4)^2} = \frac{GM_e \times 16}{80 \times R_e^2} =\frac{GM_e}{R_e^2} \times \frac{16}{80} =g_e \times \frac{1}{5}$

$g_m= \frac{g_e}{5}= \frac{9.8}{5}\ m/s^2 =1.96\ m/s^2$

So acceleration due to gravity will be 1.96 m/s² on the surface of moon.