A model is developed to establish the relationship between the critical gyration radius k of the primary component and the mass ratio (q) by considering the different dimensionless gyration radii of main-sequence stars with varying masses. The next step involves obtaining the low mass ratio limit ( \({q_{\text{min}}} = 0.038 \sim 0.041\) for overcontact degree \(f = 0\) ~ 1) of W UMa-type contact binaries. Furthermore, the radial density distributions are estimated within the range of \(0.3 M_{\odot } \sim 4.0 M_{\odot }\) , based on the mass-radius relationship of main-sequence stars. Subsequently, the physical meaning of the minimum k value is proposed, which leads to an explanation for the cause of the minimum mass ratio. Finally, a stability criterion is proposed, which is based on both the mass ratio (q) and the total mass of the two components ( \(M_{tot}\) ).
