A liquid of density `rho` comes out with a velocity `v` from a horizontal tube of area of cross-section `A`. The reaction force exerted by the liquid on the tube is `F`. Choose the incorrect option.

Options

A. `F prop v`
B. `F prop v^2`
C. `F prop A`
D. `F prop rho`

Explanation

To solve the problem, we need to analyze the relationship between the reaction force \( F \) exerted by the liquid on the tube and the various parameters given: density \( \rho \), velocity \( v \), and cross-sectional area \( A \).

### Step-by-Step Solution:

1. **Understanding the Flow of Liquid**:
- The liquid is flowing out of a tube with a certain velocity \( v \) and has a density \( \rho \). The area of cross-section of the tube is \( A \).

2. **Calculating Mass Flow Rate**:
- The mass flow rate \( \dot{m} \) of the liquid can be calculated using the formula:
\[ \dot{m} = \rho \cdot A \cdot v \]
- Here, \( \dot{m} \) represents the mass of liquid flowing out per unit time.

3. **Applying Newton's Second Law**:
- According to Newton's second law, the force exerted by the liquid can be related to the change in momentum. The momentum per unit time (which is the force) is given by:
\[ F = \dot{m} \cdot v = (\rho \cdot A \cdot v) \cdot v = \rho \cdot A \cdot v^2 \]

4. **Identifying Relationships**:
- From the equation \( F = \rho \cdot A \cdot v^2 \), we can derive the following relationships:
- \( F \) is proportional to \( v^2 \): \( F \propto v^2 \)
- \( F \) is proportional to \( A \): \( F \propto A \)
- \( F \) is proportional to \( \rho \): \( F \propto \rho \)

5. **Choosing the Incorrect Option**:
- The question asks to choose the incorrect option. The relationships derived indicate that:
- \( F \) is proportional to \( v^2 \) (correct)
- \( F \) is proportional to \( A \) (correct)
- \( F \) is proportional to \( \rho \) (correct)
- Any statement suggesting \( F \) is proportional to \( v \) (not \( v^2 \)) would be incorrect.

### Conclusion:
The incorrect option is the one that states \( F \) is proportional to \( v \) instead of \( v^2 \).