Problem 1.131

The potential energy of a particle in a certain field has the form $U=a / r^{2}-b / r,$ where $a$ and $b$ are positive constants, $r$ is the distance from the centre of the field. Find: (a) the value of $r_{0}$ corresponding to the equilibrium position of the particle; examine whether this position is steady; (b) the maximum magnitude of the attraction force; draw the plots $U(r)$ and $F_{r}(r)$ (the projections of the force on the radius vector $\mathrm{r}$ ).