In this paper, we present the critical mass of magnetized, turbulent and rotating star-forming molecular cloud core (MCc) in the presence of magnetic tension. The critical mass of star-forming magnetized cloud is influenced by the magnetic tension, magnetic pressure and other pressures. Applying the method of theoretical modelling by taking into account the basic equations and assumptions, we formulate the critical mass of magnetized MCc in different cases. Accordingly, the minimum critical masses we find in both cases are different. Energy due to magnetic tension significantly triggers the collapse at relatively larger radius of the core. The model shows that when the initial radius of the parent cloud (Ro) is larger than that of collapsing core radius (Rcore) the magnetic tension also has the larger radius of curvature, so it plays a significant role in supporting gravity to collapse the core. The results indicate gravity without magnetic tension may not overcome magnetic pressure, turbulence pressure and pressure due to rotation. This shows the critical mass of MCc for the collapse depends on the tension force that magnetic field lines apply on the envelope. We conclude that if there is magnetic pressure in star-forming MCc, there is also unavoidable magnetic tension, which triggers the collapse of the core. If there is no magnetic tension, the magnetized MCc needs relatively larger mass and higher density within the small size to collapse.
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