Which of the following relations is NOT applicable to the rocket ?

Options

A. `vecF=vecdp//dt`
B. `vecF=Mveca`
C. `vecP=Mvecv`
D. `vecP=intvecFdt`

Answer

To determine which relation is NOT applicable to a rocket, we need to analyze the relevant equations of motion and how they apply to the rocket's propulsion system.

### Step-by-Step Solution:

1. **Understanding Rocket Propulsion**:
- A rocket propels itself by expelling exhaust gases at high speed. According to Newton's third law, for every action, there is an equal and opposite reaction. The action of expelling gas produces a thrust force that propels the rocket forward.

2. **Relevant Equations**:
- The fundamental equation of motion for a system is given by Newton's second law:
\[ F = \frac{dp}{dt} \]
where \( F \) is the net force, and \( p \) is the momentum of the system.

3. **Momentum Definition**:
- Momentum \( p \) is defined as:
\[ p = mv \]
where \( m \) is the mass and \( v \) is the velocity of the rocket.

4. **Consideration of Mass**:
- In classical mechanics, if the mass of the system is constant, we can express the force as:
\[ F = ma \]
where \( a \) is the acceleration. This is valid only when the mass does not change.

5. **Changing Mass in Rockets**:
- In the case of rockets, the mass is not constant because the rocket burns fuel, which decreases its mass over time. Therefore, the relation \( F = ma \) is not applicable in this scenario since it assumes a constant mass.

6. **Valid Relations**:
- The equation \( F = \frac{dp}{dt} \) remains valid regardless of whether the mass is changing or constant.
- The relation \( p = mv \) is also always valid as it defines momentum.

7. **Conclusion**:
- The relation that is NOT applicable to the rocket is:
\[ F = ma \]
because this equation assumes a constant mass, which is not the case for a rocket as it expels fuel.

### Final Answer:
The relation that is NOT applicable to the rocket is \( F = ma \).