Assertion : Pressure has the dimensions of energy density.
Reason : Energy density = `("energy")/("volume")=(["ML"^(2)"T"^(-2)])/(["L"^(3)])`
`=["ML"^(-1)"T"^(-2)]="pressure"`

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

### Step 1: Understand the Assertion
The assertion states that "Pressure has the dimensions of energy density." We need to verify if this statement is true.

### Step 2: Understand the Reason
The reason provided is that "Energy density = (energy)/(volume)". We will calculate the dimensions of energy density to see if it matches the dimensions of pressure.

### Step 3: Find the Dimensional Formula for Energy
The dimensional formula for energy is given by:
\[ \text{Energy} = \text{mass} \times \text{(velocity)}^2 = [M][L^2][T^{-2}] \]
Thus, the dimensional formula for energy is:
\[ [E] = [M][L^2][T^{-2}] \]

### Step 4: Find the Dimensional Formula for Volume
The dimensional formula for volume is:
\[ \text{Volume} = \text{length}^3 = [L^3] \]

### Step 5: Calculate the Dimensional Formula for Energy Density
Now, we can calculate the dimensional formula for energy density:
\[ \text{Energy Density} = \frac{\text{Energy}}{\text{Volume}} = \frac{[M][L^2][T^{-2}]}{[L^3]} = [M][L^{-1}][T^{-2}] \]
So, the dimensional formula for energy density is:
\[ [E_D] = [M][L^{-1}][T^{-2}] \]

### Step 6: Find the Dimensional Formula for Pressure
Pressure is defined as force per unit area. The dimensional formula for force is:
\[ \text{Force} = \text{mass} \times \text{acceleration} = [M][L][T^{-2}] \]
The dimensional formula for area is:
\[ \text{Area} = [L^2] \]
Thus, the dimensional formula for pressure is:
\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{[M][L][T^{-2}]}{[L^2]} = [M][L^{-1}][T^{-2}] \]

### Step 7: Compare the Dimensional Formulas
From the calculations:
- The dimensional formula for energy density is \([M][L^{-1}][T^{-2}]\).
- The dimensional formula for pressure is also \([M][L^{-1}][T^{-2}]\).

### Conclusion
Since both the assertion and the reason yield the same dimensional formula, we can conclude that both the assertion and the reason are correct. Therefore, the answer to the question is that both the assertion and reason are correct, and the reason is a correct explanation of the assertion.

### Final Answer
Both assertion and reason are correct, and the reason is a correct explanation of the assertion.

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