Hello, I would really appreciate if someone helped me to figure this out. Suppose we have got a car A and car B. They both have got the same body (aerodynamics), tires, center of mass, the only difference is that the car B is x times heavier than car A. Now suppose they are both going around the same corner without loosing traction and without going sideways. The question is which car can go around the corner faster? My intuition tells me that the lightest car can corner faster, because car B is heavier thus it has more inertia and when going the same speed it has got higher kinetic energy. But the heaviest car should also have more friction between tires and road resulting in better traction when cornering. Do both of these effects cancel each other out?
Heavier car will also have more traction to use towards cornering by the same factor x. So both cars will be able to corner at exactly the same speed, at least in the idealized case. Realistically, less tire deformation might give a lighter car a slight advantage. Another real world consideration is that when you load the car, increasing its weight, you usually raise the center of mass as well, increasing risk of the car tipping over in a turn. But this is all about the height of CoM in relation to wheel base, and isn't directly tied to car's weight.
Yes, in the idealized situation that OP is (almost certainly) trying to ask about: centripetal force supplied by friction between tire and road, everything else the same. But note that OP also specified the same aerodynamics. If the aerodynamics are the same, then the limiting cornering speed is not independent of the mass. If there is an aerodynamic downforce (any purpose-built racecar, many high-performance road cars) then the lower the mass, the higher the limiting cornering speed will be.