We continue to investigate the dynamics of collisionless systems of particles interacting via additive $r^{-α}$ interparticle forces. Here we focus on the dependence of the radial-orbit instability on the force exponent $α$. By means of direct $N$-body simulations we study the stability of equilibrium radially anisotropic Osipkov-Merritt spherical models with Hernquist density profile and with $1\leqα<3$. We determine, as a function of $α$, the minimum value for stability of the anisotropy radius $r_{as}$ and of the maximum value of the associated stability indicator $ξ_s$. We find that, for decreasing $α$, $r_{as}$ decreases and $ξ_s$ increases, i.e. longer-range forces are more robust against radial-orbit instability. The isotropic systems are found to be stable for all the explored values of $α$. The end products of unstable systems are all markedly triaxial with minor-to-major axial ratio $>0.3$, so they are never flatter than an E7 system.

12 pages, 6 figures