Suppose V and E represent the gravitational potential and the gravitational field at a distance r from the centre of a uniform spherical shell. Evaluate 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 spherical shell of mass M and radius R , the gravitational potential V at a distance r from the centre is given by: V = - GM R for r R V = - GM r for r > R Since _ r R V = - GM R , the potential is continuous at r = R and everywhere else. Thus, statement A is false. The gravitational field E at a distance r from the centre is given by: E = 0 for r E = GM r^2 for r > R At r = R , the value of E abruptly changes from 0 to GM R^2 . The left-hand limit is 0 and the right-hand limit is GM R^2 . Since the l