A planet has double the mass of the earth and double the radius. The gravitational potential at the surface of the Earth is V and the magnitude of the gravitational field strength is g . The gravitational potential and gravitational field strength on the surface of the planet are No. Potential Field A V g 4 B 2V g 2 C V g 2 D 2V g 4

Step-by-step solution

The gravitational potential V at the surface of a planet of mass M and radius R is given by V = - GM R . The gravitational field strength g at the surface is given by g = GM R^2 . For the Earth, V_E = - GM_E R_E = V and g_E = GM_E R_E^2 = g . For the given planet, M_P = 2M_E and R_P = 2R_E . The gravitational potential at the surface of the planet is V_P = - GM_P R_P = - G(2M_E) 2R_E = - GM_E R_E = V . The gravitational field strength at the surface of the planet is g_P = GM_P R_P^2 = G(2M_E) (2R_E)^2 = 2GM_E 4R_E^