A cup filled with water has a hole in the side, through which the liquid is flowing out. If the cup is dropped from a height which of the following is/are correct?

Options

A. Water keeps coming out, flowing at the same rate as before
B. Water keeps coming out, but is will flow a bit slower than before.
C. Water keeps coming out, but start to flow upward relative to the cup
D. water stops flowing

Answer

To solve the problem of a cup filled with water that has a hole in the side and is dropped from a height, we need to analyze the situation based on the principles of fluid mechanics and the effects of gravity.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a cup filled with water, and there is a hole on the side of the cup.
- When the cup is stationary, water flows out of the hole due to the pressure difference created by the height of the water column above the hole.

2. **Effect of Dropping the Cup**:
- When the cup is dropped from a height, both the cup and the water inside it are in free fall.
- In free fall, all objects experience the same acceleration due to gravity (approximately 9.81 m/s²), and thus, the water inside the cup is also accelerating downwards at the same rate as the cup.

3. **Pressure at the Hole**:
- The flow of water out of the hole is determined by the hydrostatic pressure at the hole.
- In free fall, the effective pressure at the hole becomes zero because the water inside the cup is not supported by any opposing force (the cup and water are falling together).

4. **Conclusion on Water Flow**:
- Since the pressure at the hole is effectively zero during free fall, the water will not flow out of the hole.
- Therefore, the water does not keep flowing out at the same rate as before; in fact, it stops flowing.

5. **Evaluating the Options**:
- Based on the analysis, we can evaluate the options given in the question:
- Option A: Water keeps coming out flowing at the same rate as before - **Incorrect**.
- Option B: Water keeps coming out but flows a bit slower than before - **Incorrect**.
- Option C: Water keeps coming out but starts to flow slower - **Incorrect**.
- Option D: Water stops flowing - **Correct**.

### Final Answer:
The correct option is **D: Water stops flowing**.