Assertion (A): Relative magnetic permeability has no units and no dimmensions
Reason (R ): `mu_(r)=mu//mu_(0)`, where the symbols have their standard meaning.

Options

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

Explanation

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

### Step 1: Understand the Assertion
The assertion states that "Relative magnetic permeability has no units and no dimensions."

- Relative magnetic permeability (µr) is defined as the ratio of the permeability of a medium (µ) to the permeability of free space (µ0).
- Since it is a ratio of two quantities with the same dimensions (both are measures of permeability), the units cancel out.

### Step 2: Analyze the Reason
The reason provided is "µr = µ / µ0", where µ is the permeability of the medium and µ0 is the permeability of free space.

- This equation is indeed the definition of relative magnetic permeability.
- Since both µ and µ0 have the same dimensional formula (which is [M^-1 L^-1 T^-2 A^2]), when we take the ratio µ / µ0, the dimensions cancel out, confirming that µr is dimensionless.

### Step 3: Conclusion
Both the assertion and the reason are true statements. The reason correctly explains why the assertion is true.

### Final Answer
- Assertion (A) is true: Relative magnetic permeability has no units and no dimensions.
- Reason (R) is true: µr = µ / µ0, and it is the correct explanation for the assertion.

Thus, the correct answer is that both the assertion and the reason are true, and the reason is a correct explanation of the assertion.

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