The rate of change of momentum of a body is directly proportional to the _____

Options

A. Applied potential energy
B. Applied force
C. Applied displacement
D. Applied pressure

Answer

To solve the question "The rate of change of momentum of a body is directly proportional to the _____", we need to understand the relationship between momentum, force, and acceleration as described by Newton's second law of motion.

### Step-by-Step Solution:

1. **Understanding Momentum**:
- Momentum (p) is defined as the product of mass (m) and velocity (v):
\[ p = m \cdot v \]

2. **Rate of Change of Momentum**:
- The rate of change of momentum can be expressed mathematically as:
\[ \frac{dp}{dt} = \frac{d(m \cdot v)}{dt} \]
- If the mass is constant, this simplifies to:
\[ \frac{dp}{dt} = m \cdot \frac{dv}{dt} \]

3. **Relating to Force**:
- According to Newton's second law of motion, the force (F) acting on an object is equal to the rate of change of momentum:
\[ F = \frac{dp}{dt} \]
- Therefore, we can say:
\[ \frac{dp}{dt} \propto \frac{dv}{dt} \]
- This indicates that the rate of change of momentum is directly proportional to the rate of change of velocity.

4. **Conclusion**:
- Since force is also defined as the mass times the acceleration (which is the rate of change of velocity), we can conclude that:
\[ \frac{dp}{dt} \propto F \]
- Hence, the rate of change of momentum of a body is directly proportional to the applied force.

### Final Answer:
The rate of change of momentum of a body is directly proportional to the **applied force**.

---