Assertion : The magnitude of the displacement for a course of motion may be zero.
Reason : The path length for the corresponding course of motion is zero.

Options

A. A. If both assertion and reason are trure and reason is the correct explanation of assertion.
B. B. If both assertion and reason are true but reason is not the correct explanations of assertion.
C. C. If assertion is true but reason is false.
D. D. If both assertion and reason is false

Explanation

To solve the question, we need to analyze the assertion and the reason given.

**Assertion:** The magnitude of the displacement for a course of motion may be zero.

**Reason:** The path length for the corresponding course of motion is zero.

### Step-by-Step Solution:

1. **Understanding Displacement:**
- Displacement is defined as the shortest distance from the initial position to the final position, along with a direction. It is a vector quantity.
- If an object returns to its starting point after moving, the displacement is zero because the initial and final positions are the same.

2. **Example of Zero Displacement:**
- Consider an object that starts at point O, moves to point P, and then returns back to point O.
- In this case, the initial position (O) and final position (O) are the same, hence the displacement is zero.

3. **Understanding Path Length:**
- Path length, on the other hand, is the total distance traveled by the object irrespective of its initial and final positions. It is a scalar quantity.
- In the example above, the object travels from O to P and then back to O, covering a distance OP and then PO. Therefore, the total path length is 2OP, which is not zero.

4. **Analyzing the Reason:**
- The reason states that the path length for the corresponding course of motion is also zero. This is incorrect because, as shown, the path length is actually 2OP, which is greater than zero.

5. **Conclusion:**
- The assertion is true because it is possible for displacement to be zero when the initial and final positions are the same.
- The reason is false because the path length is not zero; it is equal to the total distance traveled.

### Final Answer:
- The assertion is true, but the reason is false. Therefore, the correct option is that the assertion is true and the reason is false.

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