Answer
(a) The first rod is an insulator.
(b) The second rod is negatively charged.
Work Step by Step
(a) When the first rod is rubbed with fur, electrons move from the fur onto the rod which makes the rod negatively charged. If the first rod is a conductor, mobile electrons from the conductor would move quickly back onto the fur to eliminate any potential difference between the two objects. If the first rod is a conductor, it would be difficult to build up a negative charge by rubbing it with another object. Therefore, the first rod must be an insulator.
(b) Since there is a repulsive force between the two rods, the second rod must also be negatively charged.