Assuming, g_ (Moon) = ( 1 6 ) g_ Earth and D_ (Moon) = ( 1 4 ) D_ Earth , where g and D are the acceleration due to gravity and diameter respectively, the escape velocity from the Moon is

Step-by-step solution

As we know, escape velocity, v_ e = 2 g R Let v_ m be escape velocity from moon and v_ e be the escape velocity from Earth. Then, v_ m v_ e = 2 g_ m R_ m 2 g_ e R_ e = g_ m D_ m g_ e D_ e ( D=2 R) = g_ e 6 D_ e 4 g_ e D_ e = 1 24 v_ m = v_ e 24 = 11.2 24 ~km / s ( v_ e =11.2 ~km / s )