The dimensional formula of radiation pressure is

Options

A. `[MLT^(-2)]`
B. `[ML^(-1)T^(-2)]`
C. `[M^(-2)T^(-2)]`
D. `[ML^(2)T^(-2)]`

Answer

To find the dimensional formula of radiation pressure, we start by understanding the definition of pressure and how it relates to radiation pressure.

### Step-by-Step Solution:

1. **Understanding Pressure**:
Pressure is defined as force per unit area. Mathematically, this can be expressed as:
\[ P = \frac{F}{A} \]
where \( P \) is pressure, \( F \) is force, and \( A \) is area.

2. **Dimensional Formula of Force**:
The dimensional formula of force can be derived from Newton's second law, which states that force is mass times acceleration:
\[ F = m \cdot a \]
The dimensional formula for mass \( m \) is \( [M] \), and for acceleration \( a \) (which is change in velocity over time) is:
\[ a = \frac{[L][T^{-2}]} \]
Therefore, the dimensional formula for force \( F \) is:
\[ [F] = [M][L][T^{-2}] = [M L T^{-2}] \]

3. **Dimensional Formula of Area**:
Area \( A \) is defined as length squared:
\[ A = L^2 \]
Thus, the dimensional formula for area is:
\[ [A] = [L^2] \]

4. **Combining to Find Pressure**:
Now, substituting the dimensional formulas of force and area into the pressure formula:
\[ [P] = \frac{[F]}{[A]} = \frac{[M L T^{-2}]}{[L^2]} = [M L^{-1} T^{-2}] \]

5. **Conclusion**:
Therefore, the dimensional formula of radiation pressure is:
\[ [P] = [M L^{-1} T^{-2}] \]

### Final Answer:
The dimensional formula of radiation pressure is \( [M L^{-1} T^{-2}] \).