If escape velocity on earth surface is 11.1 ~km / h , then find the escape velocity on moon surface. If mass of moon is 1 81 times of mass of earth and radius of moon is 1 4 times radius of earth.

Step-by-step solution

Given, Escape velocity on the surface of earth, v _ e =11.1 ~km / h i.e. aligned & v _ e = 2 gR _ e & v _ e = 2 GM _ e R _ e aligned Mass of moon, M_m= M_e 81 Radius of moon, R _ m = R _ e 4 Escape velocity on the surface of moon aligned & v_m= 2 G M_m R_m = 2 G M e 81 R_e 4 & = 2 2 9 GM _ c R _ c = 2 9 2 GM _ c R _ c = 2 9 v _ e = 2 9 11.1=2.46 ~km / h aligned