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 \(\mathrm{r}\) ).