Final answer:
After touching Object 2 with a positively-charged rod, induced polarization causes a redistribution of charges that leaves both objects with an excess of like charges facing each other, resulting in electrostatic repulsion.
Step-by-step explanation:
The objects repel after Object 2 is touched by the positively-charged insulated rod because of induced polarization. Initially, both objects are neutral, but when the charged rod comes near Object 2, it causes a redistribution of charges. Negative charges are attracted towards the rod, while positive charges are repelled to the far side of the object. When the rod is removed, Object 2 is left with a net positive charge on the side facing away from where the rod was. If Object 1 is close enough, it will experience polarization too, with positive charges repelled and negative charges attracted towards Object 2. Once the rod is taken away and the objects can no longer realign their charges, if any charge transfer took place, they will repel each other because they are now both positively charged on the sides facing each other, which leads to electrostatic repulsion.
This phenomenon illustrates the principle that like charges repel, which is a foundational concept in electrostatics. When Object 2 is touched by the positively-charged rod, it creates a situation where Object 2 either becomes positively charged by induction, or it has enough positive charge shifted towards the side away from Object 1, leading to repulsion between the two objects.