You are given two metal spheres mounted on portable insu-
lating supports. find a way to give them equal and opposite
charges. you may use a glass rod rubbed with silk but may
not touch it to the spheres. do the spheres have to be of equal
size for your method to work?

The spheres in the experiment could not be of equal size.

Explanation:

This is the concept of Electrostatics. The two metal spheres are placed on portable insulated stand so initially both have charge, q = 0. We thought to create equal and opposite charges on both the metal spheres without touching the charged glass rod to these spheres. First of all let us hold the rod at a distance R from any of the insulated sphere, making it closer to the spheres the phenomenon of induction arises. Finally the sphere near the rod will have induced opposite charges and the other sphere which is away from rod will get induced same charge of the rod. And in this process we will get opposite and equal charges in the spheres without touching them. No, it is not necessary to be the spheres of equal size.