Assertion : `sqrt(("Modulus of elasticity")/("Density")` has the unit `"ms"^(-1)`.
Reason : Acceleration has the dimensions of `(1)/((sqrt(epsilon_(0)mu_(0)))t)`.

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.

Explanation

To solve the problem, we need to analyze both the assertion and the reason provided in the question step by step.

### Step 1: Analyze the Assertion
The assertion states that \(\sqrt{\frac{\text{Modulus of Elasticity}}{\text{Density}}}\) has the unit of \( \text{ms}^{-1} \).

1. **Modulus of Elasticity (E)**:
- The modulus of elasticity is defined as stress divided by strain.
- Stress is defined as force per unit area. The dimensions of force (F) are given by:
\[ [F] = [M][L][T^{-2}] \]
- Area (A) has dimensions:
\[ [A] = [L^2] \]
- Therefore, the dimensions of stress are:
\[ [\text{Stress}] = \frac{[F]}{[A]} = \frac{[M][L][T^{-2}]}{[L^2]} = [M][L^{-1}][T^{-2}] \]
- Since strain is dimensionless, the dimensions of modulus of elasticity (E) are:
\[ [E] = [M][L^{-1}][T^{-2}] \]

2. **Density (\(\rho\))**:
- Density is defined as mass per unit volume. The dimensions of density are:
\[ [\rho] = \frac{[M]}{[V]} = \frac{[M]}{[L^3]} = [M][L^{-3}] \]

3. **Calculate Dimensions of \(\sqrt{\frac{E}{\rho}}\)**:
- We need to find the dimensions of \(\sqrt{\frac{E}{\rho}}\):
\[ \sqrt{\frac{E}{\rho}} = \sqrt{\frac{[M][L^{-1}][T^{-2}]}{[M][L^{-3}]}} = \sqrt{\frac{[L^{-1}][T^{-2}]}{[L^{-3}]}} = \sqrt{[L^{2}][T^{-2}]} = [L][T^{-1}] \]
- The dimensions \([L][T^{-1}]\) correspond to the unit of velocity, which is \( \text{ms}^{-1} \).

### Conclusion for Assertion:
The assertion is true since \(\sqrt{\frac{\text{Modulus of Elasticity}}{\text{Density}}}\) indeed has the unit of \( \text{ms}^{-1} \).

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### Step 2: Analyze the Reason
The reason states that acceleration has the dimensions of \(\frac{1}{\sqrt{\epsilon_0 \mu_0} \cdot t}\).

1. **Understanding \(\epsilon_0\) and \(\mu_0\)**:
- The product \(\epsilon_0 \mu_0\) is related to the speed of light \(c\) in vacuum:
\[ c = \frac{1}{\sqrt{\epsilon_0 \mu_0}} \]
- Therefore, \(\sqrt{\epsilon_0 \mu_0} = \frac{1}{c}\).

2. **Substituting into the Reason**:
- The reason can be rewritten as:
\[ \frac{1}{\sqrt{\epsilon_0 \mu_0} \cdot t} = \frac{c}{t} \]
- The dimensions of \(c\) are:
\[ [c] = [L][T^{-1}] \]
- Thus, the dimensions of \(\frac{c}{t}\) are:
\[ \frac{[L][T^{-1}]}{[T]} = [L][T^{-2}] \]
- The dimensions \([L][T^{-2}]\) correspond to acceleration.

### Conclusion for Reason:
The reason is true because it correctly identifies the dimensions of acceleration.

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### Final Conclusion:
Both the assertion and the reason are true. However, the reason does not provide a correct explanation for the assertion. Therefore, the answer is:

**B**: Both assertion and reason are true, but the reason is not the correct explanation of the assertion.

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