Assertion : `sqrt(("Magnetic dipole moment "xx" moment induction")/("Moment of inertia")`
Dimensional formula `["M"^(0)"L"^(0)"T"]`
Reason : The given dimension is that of frequency.

Options

A. If both Assertion and Reason are correct and Reason is the correct explaination of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explaination of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

To solve the problem, we need to analyze the assertion and the reason provided. We will calculate the dimensional formula of the expression given in the assertion and then compare it to the reason.

### Step-by-Step Solution:

1. **Identify the quantities involved:**
- Magnetic dipole moment (denote as \( \mu \))
- Magnetic induction (denote as \( B \))
- Moment of inertia (denote as \( I \))

2. **Write the dimensional formulas for each quantity:**
- The dimensional formula for **magnetic dipole moment** \( \mu \) is:
\[ [\mu] = [L^2 T^{-1} A] \]
- The dimensional formula for **magnetic induction** \( B \) is:
\[ [B] = [M T^{-2} A^{-1}] \]
- The dimensional formula for **moment of inertia** \( I \) is:
\[ [I] = [M L^2] \]

3. **Construct the expression given in the assertion:**
The assertion states:
\[ \sqrt{\frac{\mu \cdot B}{I}} \]

4. **Substitute the dimensional formulas into the expression:**
\[ \text{Dimension of } \mu \cdot B = [L^2 T^{-1} A] \cdot [M T^{-2} A^{-1}] = [M L^2 T^{-3}] \]
Now, substituting this into the expression:
\[ \frac{\mu \cdot B}{I} = \frac{[M L^2 T^{-3}]}{[M L^2]} = [T^{-3}] \]

5. **Taking the square root:**
\[ \sqrt{[T^{-3}]} = [T^{-3/2}] \]

6. **Final dimensional formula:**
The final dimensional formula is:
\[ [M^0 L^0 T^{-3/2}] \]
This indicates that the assertion is incorrect since it claims the dimensional formula is \([M^0 L^0 T^0]\), which is dimensionless.

7. **Evaluate the reason:**
The reason states that the given dimension is that of frequency. The dimensional formula for frequency is:
\[ [T^{-1}] \]
Since our derived dimension \([T^{-3/2}]\) does not match the dimension of frequency, the reason is also incorrect.

### Conclusion:
- The assertion is **false**.
- The reason is **false**.

### Final Answer:
The assertion is false, and the reason is false.