The correct statement that best predicts what will happen to the charge on the hollow metal sphere after being touched by the negatively charged rubber rod is:
"It will distribute itself evenly over the surface of the sphere, because like charges repel and the sphere is a conductor."
When a charged object, like the rubber rod, comes into contact with a conductor (in this case, the metal sphere), the excess charge (negative charge from the rod) will redistribute itself over the surface of the conductor. This happens due to the repulsion between like charges. Since the sphere is hollow and a conductor, the negative charges will spread out evenly across the outer surface to minimize their potential energy, as charges repel each other. The nature of conductors allows charges to move freely, leading to an even distribution rather than remaining at the point of contact.