What will be the acceleration due to gravity on the surface of the moon if its radius were (1/4) th the radius of earth and its mass (1/80) th the mass of earth ? What will be the escape velocity on the surface of moon if it is 11.2 km / s on the surface of the earth ? G(iven that `g = 9 . 8 m//s^(-2)` )

Explanation

As on the surface of planet `g = ((GM)/(R^(2)))`
`(g_(M))/( g_(g)) = (M_(M))/(M_(B)) xx ((R_(g))/(R_(m)))^(2) = (1)/(80) xx (4)^(2) = (1)/(5)`
`:. g_(M) = (g_(g))/( 5) = (9 . 8)/( 5) = 1. 96 m // s^(2)`
Furthermore as escape velocity `v_(e) = sqrt((2 GM // R))`
So, `(v_(M))/( v_(B)) = sqrt((M_(M))/(M_(B))xx (R_(E))/(R_(M))) = sqrt((1)/(80) xx 4) = (1)/(sqrt(20))`
i.e. `v_(M) = ((v_(E))/(sqrt(20))) = = ((11.2)/( 4 . 47)) = 2. 5 km //s`