Muon capture on the 2H, 3H and 3He nuclei is investigated using
the state-of-the-art nucleon-nucleon chiral potential with
a semi-local regularization up to the fifth order of chiral expansion and with the semi-phenomenological AV18 and Urbana IX forces.
Despite neglecting, in the case of the chiral force, the three-nucleon forces and using a simple model of the weak current,
the obtained results show a small cut-off dependence, which is
an important and desirable feature of this recently developed
potential. This observation is in agreement with results worked out
from the strong and electromagnetic sectors. Values of the capture
rates obtained with the chiral interaction are in good agreement with ones obtained with the AV18 force and the same model of weak current.