if you charge a rubber rod with a piece of fur and bring the rubber rod close to the top of the gold-leaf electroscope, is it induction or polarization?

It is induction

Induction also will work on an insulator with no net charge on the object by pulling the like charges toward and repelling the unlike charges. That sort of induction is called polarization.

When you charge a rubber rod by rubbing it with fur, electrons are transferred from the fur to the rod, leaving the rod negatively charged and the fur positively charged.

If you bring the negatively charged rubber rod close to the top of the gold-leaf electroscope, two phenomena can occur: induction and polarization.

Induction is when the presence of a charged object influences the distribution of charges within a neutral or insulated object. In this case, the negatively charged rubber rod repels the electrons in the gold-leaf electroscope, causing them to move away from the top. This creates a temporary separation of charges, with the bottom of the electroscope becoming negatively charged and the top becoming positively charged. However, the charges do not permanently remain separated, as there is no physical connection between the rubber rod and the electroscope.

Polarization, on the other hand, refers to the alignment of dipoles within a molecule or material in response to an external electric field. In this scenario, the gold-leaf of the electroscope is a conductor, and when the negatively charged rubber rod is brought close to it, the electrons in the gold-leaf are repelled to the bottom and the positive charges (ions) are attracted towards the top. This creates a separation of charges within the gold-leaf, without any permanent transfer of charge.

So, when you bring the charged rubber rod close to the top of the gold-leaf electroscope, it is primarily polarization rather than induction that occurs.