Answer
See the detailed answer below.
Work Step by Step
This experiment is similar to the one in which you bring a charged pole near a neutral metal sphere. In both cases, whether the rod is positively charged or negatively charged, it will polarize the sphere and it will be attracted to it.
The same thing happens here, in both cases, whether we bring the north pole or the south pole, the piece of the non-magnetized iron will be polarized and attract to the magnet.
We know that the magnetic field is produced by a permanent magnet, which is a result of the oriented spinning of the electrons.
We also know that the unmagnetized piece of iron also contains spinning electrons, but they are not aligned they are randomly oriented which makes the net magnetic moment zero.
But each one of them experiences a torque in the field of the permanent magnet. This torque tends to align the domains with the external field of the permanent magnet.
This process creates an induced net magnetic moment. And hence, the piece of iron has an induced north pole downward and south pole upward, as shown in the figure below. And the induced south pole faces the north pole of the permanent magnet and this creates an attractive force between the piece of iron and the magnet.
This force pulls the piece up toward the magnet.
In the figures below, we represented the magnetic moment of the electrons in the front lines of both the magnet and the piece of iron by arrows.
