2. Central conservative forces. (a) In the lectures we showed that if a central force F(r) = fl"- is conservative then (13} f can only depend on the magnitude of r, f = f (7'), since otherwise F95 or F9 would be nonzero. Show that the converse statement also holdsii.e., that if a force F (r) is central and spherically symmetric then it is conservativ%by demonstrating V X F = 0 using Cartesian coordinates and (for the fun of it) using spherical polar coordinates, for which A 1 5' _ 6' n 1 8 1 a V X A rrsin6[(S1neA)_ 149] + 9 [rsinglh ;E (TAQ5) n 1 8 8 +; [E (TAQ) @147} . (2) Find the force corresponding to the potential energy U = k/r, then check that, indeed, V X F = 0