Assertion: A given force applied in turn to a number of different masses may cause the same rate of change in momentum in each but not the same acceleration to all.
Reason: `F=(dp)/(dt)` and `a=F/m`

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

To solve the question, we need to analyze the assertion and the reason provided:

**Assertion:** A given force applied in turn to a number of different masses may cause the same rate of change in momentum in each but not the same acceleration to all.

**Reason:** \( F = \frac{dp}{dt} \) and \( a = \frac{F}{m} \)

### Step-by-Step Solution:

1. **Understanding the Assertion:**
- The assertion states that if we apply the same force to different masses, they can experience the same rate of change in momentum but will not necessarily have the same acceleration.
- This is based on the relationship between force, mass, and acceleration.

2. **Using the Definition of Force:**
- According to Newton's second law, force is defined as the rate of change of momentum:
\[ F = \frac{dp}{dt} \]
- Here, \( dp \) represents the change in momentum and \( dt \) represents the change in time.

3. **Applying the Same Force to Different Masses:**
- Let’s consider two different masses, \( m_1 \) and \( m_2 \).
- If we apply the same force \( F \) to both masses, we can write:
\[ F = \frac{dp_1}{dt} \quad \text{and} \quad F = \frac{dp_2}{dt} \]
- This implies that the rate of change of momentum for both masses can be equal:
\[ \frac{dp_1}{dt} = \frac{dp_2}{dt} \]

4. **Relating Force, Mass, and Acceleration:**
- From Newton's second law, we also know:
\[ F = m \cdot a \]
- Rearranging gives us:
\[ a = \frac{F}{m} \]
- For mass \( m_1 \):
\[ a_1 = \frac{F}{m_1} \]
- For mass \( m_2 \):
\[ a_2 = \frac{F}{m_2} \]

5. **Comparing Accelerations:**
- Since \( m_1 \) and \( m_2 \) are different, the accelerations \( a_1 \) and \( a_2 \) will also be different:
\[ a_1 \neq a_2 \quad \text{if} \quad m_1 \neq m_2 \]
- This shows that while the same force can cause the same rate of change in momentum, it does not result in the same acceleration for different masses.

6. **Conclusion:**
- Therefore, both the assertion and the reason are correct, and the reason correctly explains the assertion.

### Final Answer:
Both the assertion and reason are correct, and the reason is a correct explanation for the assertion.