in what direction will a freely suspended magnet come to rest?

downward.

A freely suspended magnet, also known as a compass needle, comes to rest in a direction aligned with Earth's magnetic field. To understand why, we need to know a bit about Earth's magnetic field and how magnets behave.

The Earth acts as a giant magnet, with its magnetic field extending from the North Magnetic Pole to the South Magnetic Pole. This field exerts a force on magnetic objects, such as a compass needle, causing it to align with the magnetic field lines.

So, to determine the direction in which a freely suspended magnet comes to rest, you can follow these steps:

1. Take a compass, which consists of a thin, lightweight magnet mounted on a pivot point so it can freely rotate.
2. Observe the orientation of the compass needle before any external influence.
3. Due to Earth's magnetic field, the magnetized needle will align itself in a north-south direction, with one end, usually marked with an "N" for north, pointing towards the Earth's magnetic North Pole, and the other end pointing towards the South Pole.
4. The north-seeking end of the compass needle always points towards magnetic north, which is not exactly aligned with Earth's geographic North Pole but is close to it. This is because Earth's magnetic field is not perfectly aligned with its rotational axis.
5. Therefore, if you are in the Northern Hemisphere, the freely suspended magnet needle will come to rest pointing roughly towards the geographic North Pole. In the Southern Hemisphere, it will point towards the geographic South Pole.

Keep in mind that local magnetic anomalies or strong magnetic fields from other sources may slightly affect the compass needle's alignment, but the overall principle remains the same.