Abstract The characteristics of the galactic bars that are prone to suffer a damaging impact from a massive central black hole are examined using flat stellar disks. We construct three disk model groups that consist of exponential disks with one type of velocity distribution and Kuzmin–Toomre disks with two different types of exact equilibrium distribution functions. For each disk model group, three disks that have different typical Toomre’s $Q$ values are evolved to form bars through dynamical instability. Once a bar is fully developed, a black hole (BH), whose mass is 1% of the disk mass, is adiabatically added at the center of the disk. Our results show that lower-amplitude bars, that is weaker bars, are dissolved more easily by that BH. We have found that this destructibility is rooted in the characteristic feature that the bar formed spontaneously becomes shorter in length and rounder in shape with decreasing bar amplitude. Since such weaker bars are found to originate from colder disks in each disk model group, it follows that for a given form of velocity structure, the coldness of an initial disk determines whether the bar produced in that disk is favorable to dissolution induced by a massive central BH. In addition, the existence of bar-dissolved galaxies of the kind studied here is also discussed.