The radius of the planet is double that of the earth, but their average densities are same. V _ p and V_E are the escape velocities of planet and earth respectively. If V_p V_E =x , the value of ' x ' is

Step-by-step solution

Escape velocity is given by, aligned v _ c & = 2 GM R & = 2 G R 4 3 R ^3 = 8 G 3 R ^2 = 8 G 3 R aligned As the planets have the same density; array ll & V _ e R & ~V _ P ~V _ E = R _ P R _ E = 2 R R =2 & ~V _ P ~V _ E =2 & X =2 array