The solar constant is defined as the energy incident per unit area per second. The dimensional formula for solar constant is

Options

A. `[M^(0)L^(0)T^(0)]`
B. `[MLT^(-2)]`
C. `[ML^(2)T^(-2)]`
D. `[ML^(0)T^(-3)]`

Explanation

To find the dimensional formula for the solar constant, we will follow these steps:

### Step 1: Understand the Definition
The solar constant is defined as the energy incident per unit area per second. This means we need to express it in terms of energy, area, and time.

### Step 2: Write the Expression
From the definition, we can express the solar constant (S) as:
\[ S = \frac{\text{Energy}}{\text{Area} \times \text{Time}} \]

### Step 3: Identify the Dimensions
We need to identify the dimensions of each component:
- **Energy (E)**: The dimensional formula for energy is given by \( [E] = ML^2T^{-2} \).
- **Area (A)**: The dimensional formula for area is \( [A] = L^2 \).
- **Time (T)**: The dimensional formula for time is \( [T] = T \).

### Step 4: Substitute the Dimensions
Now, substituting the dimensions into the expression for the solar constant:
\[ S = \frac{[E]}{[A] \times [T]} = \frac{ML^2T^{-2}}{L^2 \times T} \]

### Step 5: Simplify the Expression
Now we simplify the expression:
\[ S = \frac{ML^2T^{-2}}{L^2T} = ML^2T^{-2} \cdot \frac{1}{L^2T} \]
When we simplify this, the \(L^2\) in the numerator and denominator cancels out:
\[ S = M \cdot T^{-2} \cdot T^{-1} = M \cdot T^{-3} \]

### Step 6: Write the Final Dimensional Formula
Thus, the dimensional formula for the solar constant is:
\[ S = ML^0T^{-3} \]

### Conclusion
The final answer is:
\[ \text{Dimensional formula for solar constant} = ML^0T^{-3} \]