Statement I: The greater the rate of the change in the momentum vector, the greater the force applied.
Statement II: Newton's second law is `vec(F)=(dvec(p))/(dt)`.

Options

A. Statement I is true, statement II is true, Statement II is the correct explanation for statement I.
B. Statemet I is true, Statement II is true , Statement II is NOT the correct explanation for Statement I
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is true

Explanation

To solve the question, we need to analyze both statements and determine their validity based on Newton's second law of motion.

### Step-by-Step Solution:

1. **Understanding Statement I**:
- The statement claims that "The greater the rate of change in the momentum vector, the greater the force applied."
- According to Newton's second law, force is defined as the rate of change of momentum. Therefore, if the rate of change of momentum (dp/dt) is greater, it implies that the force (F) applied is also greater.
- **Conclusion**: Statement I is **True**.

2. **Understanding Statement II**:
- The statement claims that "Newton's second law is \( \vec{F} = \frac{d\vec{p}}{dt} \)".
- Newton's second law can be expressed in terms of momentum (p), where \( \vec{F} \) (force) is equal to the derivative of momentum with respect to time. This is a valid expression of Newton's second law.
- **Conclusion**: Statement II is **True**.

3. **Relationship Between the Statements**:
- Statement II provides the mathematical basis for Statement I. Since Statement II accurately describes Newton's second law, it serves as the correct explanation for Statement I.
- **Conclusion**: Statement II is the correct explanation for Statement I.

4. **Final Conclusion**:
- Both statements are true, and Statement II is the correct explanation for Statement I.

### Final Answer:
Both Statement I and Statement II are true, and Statement II is the correct explanation for Statement I.

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