A negatively-charged rod is brought close to (but does not touch) two neutral spheres that are in contact with each other but insulated from the ground. If the two spheres are then separated, what kind of charge will be on the spheres

One sphere obtains a positive charge, while the other obtains a negative charge.

Explanation:

When the negatively-charged rod is brought close to the two neutral spheres in contact with each other, the electrons in both spheres are repelled away from the rod and thus those electrons move into the second sphere farther away from the rod.

The first sphere is now short of electrons.

When the spheres are separated, the first sphere which is short of electrons now carries a net positive charge, while the other sphere which has excess electrons now carries a net negative charge.