For this third paper in the series, we studied the kinematics of the ionised gas and stars, and calculated the dynamical masses of the circumnuclear star-forming regions in the ring of the face-on spiral NGC 7742. We used high spectral resolution data from the MEGARA instrument mounted on the Gran Telescopio Canarias (GTC) to measure the kinematical components of the nebular emission lines of selected HII regions and the stellar velocity dispersions from the CaT absorption lines that allow the derivation of the associated cluster virialised masses. The emission line profiles show two different kinematical components: a narrow one with a velocity dispersion of ∼ 10 km/s and a broad one with a velocity dispersion similar to the values found for the stellar absorption lines. The derived star cluster dynamical masses range from 2.5 times 10^6 to 10.0 times 10^7 M_⊙. The comparison of gas and stellar velocity dispersions suggests a scenario where the clusters have formed simultaneously in a first star formation episode with a fraction of the stellar evolution feedback remaining trapped in the cluster, subject to the same gravitational potential as the cluster stars. Between 0.15 and 7.07 % of the total dynamical mass of the cluster would have cooled down and formed a new, younger, population of stars, responsible for the ionisation of the gas currently observed.
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