Introduction:

When a uniform rod is kept vertically on a horizontal smooth surface and then rotated slightly and released, it falls down on the horizontal surface. In this scenario, the lower end of the rod will remain at the same position on the horizontal surface where it was initially placed. This behavior can be understood by analyzing the forces acting on the rod and the concept of torque.

Explanation:

1. Initial State:
- The rod is kept vertically on a horizontal smooth surface.
- Let the lower end of the rod be denoted as point O, which is in contact with the surface.
- The rod is in equilibrium in this initial state, with no net forces or torques acting on it.

2. Rotation and Release:
- When the rod is rotated slightly and released, it starts to fall down due to the force of gravity acting on it.
- The rod experiences a clockwise torque about point O, caused by the gravitational force acting on its center of mass.
- This torque causes the rod to rotate in a clockwise direction, leading to its downward motion.

3. Conservation of Angular Momentum:
- As the rod falls down, it conserves its angular momentum.
- The initial angular momentum of the rod is zero since it is at rest.
- As the rod falls, its rotational inertia decreases due to the change in its orientation. However, its angular velocity increases to compensate for the decrease in rotational inertia, thus conserving the angular momentum.

4. Lower End Position:
- The lower end of the rod (point O) remains at the same position on the horizontal surface where it was initially placed.
- This occurs because the torque acting on the rod is only due to the gravitational force acting on its center of mass.
- The center of mass of the rod lies somewhere along the length of the rod, and it is this point that falls down and rotates about point O.
- However, the lower end of the rod (point O) does not experience any torque, as it is the point of contact with the surface.
- Therefore, the lower end remains stationary on the horizontal surface.

5. Conclusion:
In conclusion, when a uniform rod is kept vertically on a horizontal smooth surface and then rotated slightly and released, it falls down on the horizontal surface. The lower end of the rod remains at the same position on the horizontal surface where it was initially placed. This occurs because the lower end does not experience any torque and remains stationary due to its contact with the surface.