A meter stick is placed vertically at the origin on a frictionles surface. A gentle push in +x direction is given to the top most point of the rod. When it has fallen completely x-coordinate of center of rod is at

Options

A. origin
B. `-0.5m`
C. `-1m`
D. `+0.5m`

Explanation

To solve the problem, we will analyze the motion of the meter stick (rod) when it is given a gentle push in the positive x-direction and falls due to gravity.

### Step-by-Step Solution:

1. **Understanding the Initial Setup**:
- We have a meter stick placed vertically at the origin (0, 0) on a frictionless surface. The length of the stick is 1 meter, so its endpoints are at A(0, 0) and B(0, 1).

2. **Identifying the Center of Mass**:
- The center of mass (CM) of the meter stick is located at its midpoint. Since the stick is 1 meter long, the coordinates of the center of mass are:
\[ \text{CM} = \left(0, \frac{1}{2}\right) = (0, 0.5) \]

3. **Effect of the Push**:
- A gentle push is applied at the topmost point of the rod (point B) in the positive x-direction. This push will cause the rod to start falling over.

4. **Analyzing the Motion**:
- Since the surface is frictionless, there is no horizontal force acting on the center of mass of the rod. The only force acting on the rod is gravity, which acts downward.
- As the rod falls, it will rotate around its base (point A), but the center of mass will not move horizontally because there is no friction to provide a horizontal force.

5. **Final Position of the Center of Mass**:
- As the rod falls, the center of mass will move downward due to gravity, but it will remain at the same x-coordinate because there is no horizontal movement.
- Therefore, when the rod has completely fallen, the x-coordinate of the center of mass will still be:
\[ x = 0 \]

6. **Conclusion**:
- The x-coordinate of the center of the rod when it has fallen completely is at the origin (0, 0).

### Final Answer:
The x-coordinate of the center of the rod when it has fallen completely is **0**.

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