I've worked out the accelerations of each of the masses, as asked in the question, but I'm struggling with the intuition of it all. I understand that mass C will move down, and so the pulley will move with the same acceleration towards the edge of the table. My confusion relates to the following:
If the tension in the string, and therefore the net force, is the same for both mass A and mass B, they must have different accelerations. So, I gather that the lighter mass of the two will move faster towards the pulley, and the heavier one will move slower. However, surely this would cause rotation in the pulley, which would cause the heavier mass to also move away from the pulley.
I am very confused as to how this will affect the acceleration of that heavier mass. Its acceleration must be only due to the tension in the string, so how can it possibly move away from the pulley while also accelerating towards it?