Final answer:
When a positively charged object is brought near an uncharged electroscope, the leaves diverge as negative charges in the leaves are attracted to the disk, leaving them positively charged and repulsive to each other. If the electroscope was pre-charged with a positive charge and other charged objects are brought near, the leaves' behavior will indicate the nature of those objects' charges.
Step-by-step explanation:
When a positively charged object is brought near the disk of an uncharged electroscope, the electroscope's leaves, which contain negative charges, will be attracted towards the disk. As negative charges move up through the conductor to the disk, the leaves will become positively charged and repel each other due to the like charges. Hence, the leaves will diverge, indicating the presence of a charge. If the electroscope had already been charged via contact with a positively charged object, then bringing another charged object near its knob would either cause the leaves to diverge further (if the object has a like charge) or converge (if the object has an opposite charge).
Should the positively charged object be removed, the leaves of the previously uncharged electroscope would fall back down because the induced charge redistributes evenly. But if the electroscope was left with excess positive charge after being touched by the charged rod, the leaves would remain apart even after the object is removed, because there would still be repulsion between the like positive charges.