Understand the assertion

Assertion $A$: A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar of same geometry and mass.

This is a well-known effect of electromagnetic induction. As the magnet falls through the conducting pipe, the magnetic flux through sections of the pipe changes with time.

Apply Faraday’s law and Lenz’s law

Because the magnetic flux changes, eddy currents are induced in the metallic pipe.

By Lenz’s law, the direction of induced current is such that it opposes the change causing it. Hence, the magnetic field due to these eddy currents opposes the motion of the falling magnet.

Effect on the falling magnet

The magnet experiences an upward magnetic retarding force due to these induced currents. Therefore, its downward acceleration becomes less than $g$, and it takes more time to pass through the pipe.

So, Assertion $A$ is true.

Check the reason

Reason $R$: For the magnetic bar, eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar.

This statement is correct. The changing flux due to the moving magnet induces eddy currents, and their magnetic effect opposes the magnet’s motion.

So, Reason $R$ is also true.

Check whether R explains A

The assertion is true precisely because eddy currents are induced in the conducting pipe and they oppose the magnet’s fall.

Therefore, $R$ is the correct explanation of $A$.

Conclusion

The correct option is: $\boxed{D}$

Comparison with stored answer

Stored correct answer: $D$

My derived answer also gives $D$, so they match.