Suppose V and E respectively denote the gravitational potential and field at a distance r from the centre of a uniform solid sphere. Consider the following two statements: (A) The graph of V versus r is discontinuous. (B) The graph of E versus r is discontinuous.

Step-by-step solution

For a uniform solid sphere of mass M and radius R , the gravitational potential V at a distance r from the centre is given by: V = - GM 2R^3 (3R^2 - r^2) for r R V = - GM r for r R At r = R , V = - GM R from both expressions. Thus, V is a continuous function of r . The gravitational field E at a distance r from the centre is given by: E = GMr R^3 for r R E = GM r^2 for r R At r = R , E = GM R^2 from both expressions. Thus, E is also a continuous function of r . Since both V and E are continuous everywhere, the grap