Which of the following most closely depicts the correct variation of the gravitation potential, V ( r ) with distance r due to a large planet of radius R and uniform mass density? (figures are not drawn to scale)

Step-by-step solution

At inside points ( r < R ) , V = - G M 2 R 3 3 R 2 - r 2 . So at the centre, r = 0 ⇒ V = - 3 2 G M R   . At outside points r > R , V = - G M r . At surface, V = - G M R . So the gravitational potential is non-uniform and negative.