Question

Let V and E denote the gravitational potential and gravitational field at a point. It is possible to have

(a) V = 0 and E = 0

(b) V = 0 and E ≠ 0

(c) V≠ 0 and E = 0

(d) V≠ 0 and E ≠ 0.

Answer 1

All of these

EXPLANATION: 

Consider a thin spherical shell and choose r = infinity where potential is zero. At infinity V = 0, E = 0. So (a) is true. At any point outside the shell V ≠ 0 and E ≠ 0. So (d) is true. At any point inside the shell E = 0 but V ≠ 0. So (c) is true.

Keeping infinity as a reference point (b) cannot be true. But if we choose reference point just outside the shell then here V = 0 but E ≠ 0. So (b) is true.