A particle of mass m moves under a central force described by the potential \(U(r) = -\frac{k}{r^2}\), where k is a positive constant. The particle’s angular momentum about the center of force is L. What is the radius of the stable circular orbit for this particle?
1
\( r = \left(\frac{L^2}{m k}\right)^{\frac{1}{3}} \)
2
\( r = \frac{L^2}{m k} \)
3
\( r = \left(\frac{m k}{L^2}\right)^{\frac{1}{3}} \)
4
\( r = \frac{m k}{L^2} \)