A bottle of soda water is rotated in a vertical circle with the neck held in hand. The air bubbles are collected

Options

A. near the neck
B. near the bottom
C. at the middle
D. uniformly in the bottle

Answer

To solve the problem of where the air bubbles in a bottle of soda water will collect when the bottle is rotated in a vertical circle, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a bottle of soda water that is being rotated in a vertical circle. The neck of the bottle is held in hand, and we need to determine where the air bubbles will collect.

2. **Centripetal Force**:
- When the bottle is rotated, the soda experiences centripetal force directed towards the center of the circular path. This force causes the liquid inside the bottle to move in a circular motion.

3. **Behavior of the Soda**:
- As the bottle rotates, the soda will experience different forces at different points in the circle. At the top of the circle, the soda is pushed outward due to inertia, while at the bottom of the circle, it is pushed upward due to the centripetal force.

4. **Direction of Air Bubbles**:
- The air bubbles in the soda are less dense than the liquid. Therefore, they will tend to rise to the top of the liquid. When the bottle is rotated, the soda moves in a circular path, and the bubbles will move in the opposite direction to the soda.

5. **Conclusion**:
- Since the bubbles will rise to the top of the liquid, and considering the rotation, the bubbles will collect at the neck of the bottle. This is because when the soda is at the top of the circle, the bubbles will be pushed downwards, and when the soda is at the bottom, the bubbles will rise to the neck.

### Final Answer:
The air bubbles will collect near the neck of the bottle.

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