A: When a bar magnet is dropped into a vertical long hollow metallic tube, the magnet ultimately moves with zera acceleration.
R: The magnet falling into metallic tube causes the eddy currents in the metal tube, so the motion of the magnet is damped.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion.
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion.
C. If Assertion is true statement but Reason is false.
D. If both Assertion and Reason are false statements.

Answer

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- A bar magnet is dropped into a long hollow metallic tube. We need to analyze the motion of the magnet as it falls through the tube.

2. **Initial Motion of the Magnet**:
- When the magnet is initially dropped, it experiences gravitational force acting downwards. This causes it to accelerate downwards.

3. **Magnetic Field Interaction**:
- As the magnet falls, it creates a changing magnetic field around it. The magnetic field lines of the bar magnet extend from its north pole to its south pole. The motion of the magnet through the metallic tube causes these magnetic field lines to cut through the walls of the tube.

4. **Induction of Eddy Currents**:
- According to Faraday's Law of Electromagnetic Induction, a change in magnetic flux through a conductor induces an electromotive force (EMF). In this case, the changing magnetic field due to the falling magnet induces currents in the metallic tube known as eddy currents.

5. **Effect of Eddy Currents**:
- Eddy currents flow in loops within the metallic tube. These currents create their own magnetic fields, which oppose the motion of the falling magnet according to Lenz's Law. This opposition results in a force acting upwards on the magnet.

6. **Damping of Motion**:
- The upward force due to the eddy currents acts against the gravitational force. As the magnet continues to fall, the upward force increases until it balances the downward gravitational force. This results in the magnet eventually moving with a constant velocity, meaning it has zero acceleration.

7. **Conclusion**:
- The assertion states that the magnet ultimately moves with zero acceleration, which is true. The reason provided explains that the falling magnet induces eddy currents in the tube, which dampens its motion, and this is also true. Therefore, both the assertion and reason are correct, and the reason correctly explains the assertion.

### Final Answer:
- **Assertion (A)**: True
- **Reason (R)**: True
- **Conclusion**: Both A and R are true, and R is the correct explanation of A.

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