The encounter of a nanodrop with a nanoprotrusion on a hysteresis-free surface is explored by many-body dissipative particle dynamics (MDPD) and surface evolver (SE). On a smooth surface, a nanodrop exhibits random motion but will be captured as it encounters a protrusion. For both lyophilic and lyophobic systems, there exists an attraction between the drop and the protrusion. The potential energy profiles associated with the detachment processes with and without crossing the protrusion are acquired by the determination of the displacement of the captured drop responding to the externally applied forces. It is found that the critical force and depth of the energy well of the lyophilic system are greater than those of the lyophobic system. Moreover, the drop straddling on the protrusion symmetrically is stable for the lyophilic system but becomes unstable for the lyophobic system. Our results can shed some light on the effect of surface roughness on droplet wetting.