The acceleration due to gravity on moon is 1^ th 6 times the acceleration due to gravity on earth. If the ratio of the density of earth ' e_e ' to the density of moon ' e_m ' is 5 3 then the radius of moon ' R_m ' in terms of the radius of earth ' R_e ' is

Step-by-step solution

We know g= GM R ^2 And the relation between mass and density of the planet is given by aligned & M= ( 4 3 R^3 ) & g= ( 4 G 3 ) R=K R aligned Given, g _ m = 1 6 ~g _ e and e _ m = 3 5 e _ e aligned & g_m g_e = e_m R_m e_e R_e = 1 6 & 3 R_m 5 R_e = 1 6 & R_m= 5 18 R_e aligned