A : A dimensionless quantity may have unit.
R : Two physical quantities having same dimensions, may have different units.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4).

Answer

To analyze the assertion and reason provided in the question, we will break down the concepts of dimensionless quantities and the relationship between dimensions and units.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that a dimensionless quantity may have a unit.
- By definition, a dimensionless quantity is one that does not have any physical dimensions associated with it. Examples include ratios like the coefficient of friction or angles measured in radians.
- Since dimensionless quantities do not have dimensions, they typically do not have units. Therefore, the assertion is **incorrect**.

2. **Understanding the Reason (R)**:
- The reason states that two physical quantities having the same dimensions may have different units.
- This is true. For instance, energy can be expressed in Joules, but it can also be represented in terms of other units such as Newton-meters or even in terms of mass and acceleration (e.g., kg·m²/s²).
- Different units can represent the same physical quantity as long as they are consistent with the dimensions. Therefore, the reason is **correct**.

3. **Conclusion**:
- Since the assertion is incorrect and the reason is correct, we conclude that the overall statement is false.

### Final Answer:
- Assertion (A) is false.
- Reason (R) is true.
- Therefore, the correct option is that the assertion is incorrect, and the reason is correct.

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