A rod of length l is released from the vertical position on a smooth horizontal plane. What is the nature of motion of the free end of the rod ?

Answer

To determine the nature of motion of the free end of a rod of length \( l \) released from a vertical position on a smooth horizontal plane, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Initial Position**:
- The rod is initially held vertically. When released, the center of mass of the rod will start to fall due to gravity.

**Hint**: Visualize the initial vertical position of the rod and the forces acting on it.

2. **Torque and Angular Motion**:
- As the rod falls, the gravitational force acting on its center of mass creates a torque about the pivot point (the end of the rod that remains in contact with the ground). This torque causes the rod to rotate.

**Hint**: Consider how the force of gravity acts on the center of mass and how it leads to rotation.

3. **Path of the Free End**:
- The free end of the rod will not only move downward but also horizontally due to the rotation. As the rod rotates about the pivot, the free end traces a path.

**Hint**: Think about how the free end moves in relation to the pivot point and the length of the rod.

4. **Nature of the Motion**:
- The trajectory of the free end can be analyzed. The motion of the free end will be a combination of circular motion (due to rotation) and linear motion (due to the downward fall).
- The theoretical analysis suggests that the path is circular, but experimental observations indicate that the path is elliptical.

**Hint**: Recall the difference between theoretical predictions and experimental results in physics.

5. **Conclusion**:
- Therefore, the nature of the motion of the free end of the rod is elliptical when observed experimentally.

**Hint**: Summarize the findings and relate them back to the initial conditions of the problem.

### Final Answer:
The nature of the motion of the free end of the rod is elliptical.