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This is an aspect of Lenz's law. Copper is a non magnetic substance but is a conductor. When a magnet moves through the copper pipe it induces a current known as eddy currents. There will be a magnetic field created by the current. According to Lenz's law it will oppose the motion or change which is producing it.

This results in an attractive force between the magnet and the copper pipe in which a current is induced by the falling magnet. The plastic rod is not conducting and hence it will not affect the fall.

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