What would happen to the two balls if one of them were kept positively charged and the charge on the other ball were slowly increased

If q is the charge on ball 1 and q' is the charge on other ball. At a moment if one of the ball kept positively charged and the charge on the other ball were slowly increased, the amount of change on second ball increases. As a result, the two ball moves very far apart from each other.

Also, if the magnitude of charge increases, the force of repulsion acting between them increases. Hence, this is the required solution.