Which of the following units denotes the dimensions `[ML^(2)//Q^(2)]`, where Q denotes the electric charge?

Options

A. `Wb//m^(2)`
B. Henry `(H)`
C. `H//m^(2)`
D. Weber `(Wb)`

Answer

To determine which unit denotes the dimensions \([ML^2/Q^2]\), where \(Q\) represents electric charge, we will analyze the given units step by step.

### Step-by-Step Solution:

1. **Understanding the Dimensions**:
- We need to find a unit that has the dimensions \([ML^2/Q^2]\).
- Here, \(M\) represents mass, \(L\) represents length, and \(Q\) represents electric charge.

2. **Analyzing the Given Units**:
- We will evaluate the units provided in the question to see which one matches the required dimensions.

3. **Unit 1: Weber per meter square (Wb/m²)**:
- The unit of Weber (Wb) can be expressed in terms of base units:
\[ \text{Weber} = \text{kg} \cdot \text{m}^2/\text{s}^2/\text{A} \]
- Therefore, the dimension of Weber per meter square is:
\[ \text{Wb/m}^2 = \frac{\text{kg} \cdot \text{m}^2/\text{s}^2/\text{A}}{\text{m}^2} = \frac{\text{kg}}{\text{s}^2 \cdot \text{A}} \]
- This gives us the dimensions:
\[ [M][L^0][Q^{-1}] \]

4. **Unit 2: Henry (H)**:
- The unit of Henry can be expressed as:
\[ \text{Henry} = \text{kg} \cdot \text{m}^2/\text{s}^2/\text{A}^2 \]
- The dimension of Henry per meter square is:
\[ \text{H/m}^2 = \frac{\text{kg} \cdot \text{m}^2/\text{s}^2/\text{A}^2}{\text{m}^2} = \frac{\text{kg}}{\text{s}^2 \cdot \text{A}^2} \]
- This gives us the dimensions:
\[ [M][L^0][Q^{-2}] \]

5. **Comparing with Required Dimensions**:
- Now we need to compare the dimensions we derived with the required dimensions \([ML^2/Q^2]\).
- The dimensions of Henry per meter square \([M][L^0][Q^{-2}]\) do not match \([ML^2/Q^2]\).

6. **Unit 3: Weber**:
- The dimension of Weber itself is:
\[ [M][L^2][T^{-2}][Q^{-1}] \]
- Therefore, the dimensions of Weber per meter square is:
\[ \text{Wb/m}^2 = \frac{[M][L^2][T^{-2}][Q^{-1}]}{[L^2]} = [M][L^0][T^{-2}][Q^{-1}] \]
- This does not match either.

7. **Conclusion**:
- After analyzing the units, we find that the only unit that matches the dimensions \([ML^2/Q^2]\) is **Henry per meter square**.

### Final Answer:
The unit that denotes the dimensions \([ML^2/Q^2]\) is **Henry per meter square**.