Problem F2 - Central Forces [10 Points] A particle of mass m is moving in the force field F(T) = nk 31 pn+1 (1) where k is a constant and n a positive integer (n E N) . 1. Show explicitly that F(r) is conservative and determine the potential V(r). Choose any po- tential constant such that V(r) vanishes at large distances. 2. Under which conditions for k and n can the mass m reach the center of the force field at n = 0? 3. Find the radius of circular orbits. For which values of n can these orbits be stable