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 solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states: "A dimensionless quantity may have units."

- **Explanation**: A dimensionless quantity is a quantity that has no physical dimensions (length, mass, time, etc.) associated with it. However, it can still be expressed in terms of units. For example, loudness measured in decibels (dB) is a dimensionless quantity because it is a ratio of two intensities (I/I₀). Even though it is dimensionless, it has a unit (decibels).

**Conclusion**: The assertion is true.

### Step 2: Analyze the Reason
The reason states: "Two physical quantities having the same dimensions may have different units."

- **Explanation**: This statement is also true. Different physical quantities can have the same dimensional formula but can be expressed in different units. For example, angular speed (ω) can be measured in revolutions per second (rev/s) or radians per second (rad/s), while frequency (f) is measured in hertz (Hz) or cycles per second (s⁻¹). Both ω and f have the same dimensions (T⁻¹), but their units differ.

**Conclusion**: The reason is true.

### Step 3: Determine the Relationship Between Assertion and Reason
- The assertion and reason are both true, but they are not directly related to each other. The assertion talks about dimensionless quantities having units, while the reason discusses different units for quantities with the same dimensions.

### Final Conclusion
Both the assertion and reason are true, but the reason does not serve as a correct explanation for the assertion.

### Final Answer
Both assertion and reason are true, but the reason is not a correct explanation for the assertion.

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