Answer
Both spheres and the metal rod become neutral.
Work Step by Step
Since both metal spheres and the rod are all metal and therefore conductors, when the two spheres come in contact with the rod then everything becomes neutral.
This is because when a conductor comes in contact with an excess charge, the excess charges spread out as uniform as it can throughout the material.
When the two spheres come in contact with the metal rod, the excess negative charge that the left sphere has spread out uniformly between the rod and the right sphere, and the excess positive charge that the right sphere has spreads out uniformly between the rod and the left sphere. Thus, there is an equal distribution of charge throughout the two ball-rod system and the system is neutral.
