Calculate the acceleration due to gravity on the surface of moon if mass of the moon is 1/80 times that of the Earth and diameter of the moon is 1/4 times that of the Earth.

Explanation

`M_m` = Mass of the moon = M/80 if M is mass of the Earth.
` (R_m) ` = Radius of the moon = R/4 if R is Radius of the Earth.
Acceleration due to gravity on the surface of the Earth,` g = GM//R^2 ` - (1)
Acceleration due to gravity on the surface of the moon, `g_m=GM_m// R_m^2` - (2)
` therefore ` From equation (1) and (2)
`(g_m)/(g) = (M_m)/(M) xx [ (R )/(R_m)]^2`
`(g_m)/(g) = 1/80 xx [4/1]^2`
` therefore (g_m)/(g) = 1/5`
` therefore g_m = g/5 = (9.8)/(5)`
` therefore g_m = 1.96 m//s^2`