Consider a planet whose density is same as that of the earth but whose radius is three times the radius ' R ' of the earth. The acceleration due to gravity ' g _ n ' on the surface of planet is g_n=x . g where g is acceleration due to gravity on surface, of earth. The value of ' x ' is

Step-by-step solution

array ll & As , g = GM R ^2 and M = V & g = G V R ^2 = G 4 3 R ^3 R ^2 & g R array For the planet: Radius R =3 R array ll & g _ planet = G V _ planet (3 R )^2 & where V _ planet = 4 3 (3 R )^3 & g _ planet = G 4 3 (3 R )^3 (3 R )^2 & g _ planet 3 R array g g _ planet = R 3 R ....(since is constant) array ll & g _ planet =3 ~g & x =3 array