Step 1: Understand what happens when a bar magnet is cut.
A bar magnet always consists of aligned magnetic domains.
When a magnet is cut into two parts, each part becomes a complete magnet having its own north pole and south pole.
Magnetic poles cannot exist independently. Hence, isolated magnetic monopoles are not formed.
Step 2: Identify the poles formed at the cut surface.
The original magnet has
\[
N \qquad \text{------} \qquad S
\]
After cutting at the middle, the left piece becomes
\[
N \qquad S
\]
and the right piece becomes
\[
N \qquad S.
\]
Thus, the newly created faces at the cut are
\[
S \quad \text{and} \quad N.
\]
Step 3: Determine the interaction between the two pieces.
Since the facing poles are
\[
S \quad \text{and} \quad N,
\]
they are unlike poles.
Unlike magnetic poles attract each other.
Therefore, when the two pieces are held a small distance apart, an attractive force acts between them.
Step 4: Final conclusion.
Hence, the two pieces
\[
\boxed{\text{attract each other}}
\]
and the correct option is
\[
\boxed{(2)}
\]