Answer: Object B stays neutral but becomes polarized.
Explanation: Suppose we have two spheres, The sphere A is negatively charged and the sphere B is neutral
When we put those near each other there can not be a flow of charge, so the sphere B remains neutral charged, but always in physics the energy must be minimized, this means that if the sphere A is negatively charged, then the surface of the sphere B that is near the sphere A will "accumulate" positive charge in order to "interact" with the field of the sphere A, and as one side has a positive charge, the other side of the sphere B must have the negative charge, this means that the sphere is polarized, where one of the sides has a negative charge and the other one positive, but if we separate the spheres, the sphere B will be neutral again and the charges will redistribute evenly in the sphere.