[UPSC CSE 2023] Central Force Motion and Gravitation (Q70, 10M)

(i) Derive the expressions for gravitational potentials at a point (I) outside the spherical shell, (II) inside the spherical shell. (ii) Calculate the escape velocity of a body of mass 10\text{ kg} from the surface of Moon \left( g_{\text{Moon}} = \frac{1}{6} g_{\text{Earth}} \right). Mass of Moon = 7\cdot3 \times 10^{22}\text{ kg} Radius of Moon = 1\cdot7 \times 10^6\text{ m}