Question

a bar magnet falls from height 'h' through a metal ring. Will its acceleration be equal to 'g'?

Answer 1

As the magnet falls, the magnetic flux linked with the ring changes. This sets up an induced emf and an hence an induced current in the ring. The direction of an induced current is so as to oppose the downward motion of the magnet. Hence, the acceleration of the falling magnet is less than that due to gravity.
If the ring is cut, an induced emf exists but the induced current is zero. Hence, there will be no opposing force to the falling magnet and it falls with the acceleration due to gravity.

Answer 2

There will be no opposing force to the falling magnet and it falls with the acceleration due to gravity.