[UPSC IFoS 2025] Central Force Motion and Gravitation (Q64, 15M)

A particle of mass \text{m} moves under the attractive central force \text{F} = -\frac{\text{C}}{\text{r}^{\text{n}+1}}. Find the condition for which the particle will have stable circular orbit. (\text{C} > 0, a constant).