Assertion: Separation between two bodies moving in the same direction on the ground with same acceleration, will not increase.
Reason: In this case river flow helps to cross the river.

Options

A. a.If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.
B. b.If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.
C. c.If Assertion is Trie but the Reason is False.
D. d.If both Assertion `&` Reason are false

Answer

To solve the given assertion and reason question, we will analyze both the assertion and the reason step by step.

### Step 1: Analyze the Assertion
**Assertion:** Separation between two bodies moving in the same direction on the ground with the same acceleration will not increase.

1. **Understanding the Assertion:**
- If two bodies (let's call them A and B) are moving in the same direction with the same acceleration, their relative acceleration with respect to each other is zero.
- This means that both bodies are accelerating at the same rate, and thus, if they start at the same point, they will remain at the same distance apart.

2. **Relative Velocity:**
- However, if the initial velocities of A and B are different, the relative velocity (the difference in their velocities) will not be zero.
- The formula for relative velocity is given by \( v_{AB} = u_A - u_B \), where \( u_A \) and \( u_B \) are the initial velocities of A and B respectively.

3. **Conclusion for Assertion:**
- If \( u_A \neq u_B \), then even though the acceleration is the same, the separation between A and B will increase over time due to their different initial velocities.
- Therefore, the assertion is **false**.

### Step 2: Analyze the Reason
**Reason:** In this case, river flow helps to cross the river.

1. **Understanding the Reason:**
- The reason seems to refer to a scenario involving a river and how the flow of the river can assist in crossing it.
- When crossing a river, the flow of the river can affect the trajectory of an object (like a boat) moving across it.

2. **Relevance to Assertion:**
- The flow of the river is not relevant to the assertion about the separation of two bodies moving on the ground.
- The assertion deals with bodies moving on a flat surface, while the reason discusses a scenario involving a river, which is a different context.

3. **Conclusion for Reason:**
- The reason provided does not support the assertion and is also **false**.

### Final Conclusion
- Both the assertion and the reason are false. Therefore, the correct option is **D**: Both assertion and reason are false.