Dimensions of solar constant are

Options

A. `M^1L^0T^(-3)`
B. `M^1L^1T^(-3)`
C. `M^0L^0T^(3)`
D. `M^1L^2T^(-3)`

Answer

To find the dimensions of the solar constant, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Solar Constant**:
The solar constant (S) is defined as the amount of solar energy received per unit area per unit time. Mathematically, it can be expressed as:
\[ S = \frac{E}{A \cdot T} \]
where \(E\) is the energy, \(A\) is the area, and \(T\) is the time.

2. **Identify Dimensions of Energy**:
The dimension of energy (E) can be expressed as:
\[ [E] = [ML^2T^{-2}] \]
where:
- \(M\) = mass
- \(L\) = length
- \(T\) = time

3. **Identify Dimensions of Area**:
The dimension of area (A) is given by:
\[ [A] = [L^2] \]

4. **Substitute Dimensions into the Formula**:
Now substituting the dimensions into the solar constant formula:
\[ S = \frac{[E]}{[A] \cdot [T]} = \frac{[ML^2T^{-2}]}{[L^2] \cdot [T]} \]

5. **Simplify the Expression**:
When we simplify the expression, we have:
\[ S = \frac{[ML^2T^{-2}]}{[L^2T]} = [M][L^2][T^{-2}][L^{-2}][T^{-1}] \]
This simplifies to:
\[ S = [M][T^{-3}] \]
Thus, the dimensions of the solar constant are:
\[ [S] = [M][T^{-3}] \]

### Final Answer:
The dimensions of the solar constant are \( [M][T^{-3}] \).

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