The quantities `A and B` are related by the relation, `m=A//B`, where `m` is the linear density and `A` is the force. The dimensions of `B` are of

Options

A. pressure
B. latent heat
C. work
D. None of these

Explanation

To solve the problem, we need to find the dimensions of the quantity \( B \) given the relationship \( m = \frac{A}{B} \), where \( m \) is the linear density and \( A \) is the force.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
We start with the equation:
\[ m = \frac{A}{B} \]
Here, \( m \) is the linear density, \( A \) is the force, and \( B \) is the quantity whose dimensions we need to find.

2. **Expressing Linear Density**:
Linear density \( m \) is defined as mass per unit length. Therefore, we can express it as:
\[ m = \frac{\text{mass}}{\text{length}} = \frac{M}{L} \]
where \( M \) is the dimension of mass and \( L \) is the dimension of length.

3. **Dimensional Formula of Force**:
The dimensional formula for force \( A \) is given by Newton's second law, which states that force is mass times acceleration:
\[ A = \text{mass} \times \text{acceleration} = M \cdot (LT^{-2}) = MLT^{-2} \]

4. **Substituting into the Equation**:
Now, substituting the dimensional formulas into the equation \( m = \frac{A}{B} \):
\[ \frac{M}{L} = \frac{MLT^{-2}}{B} \]

5. **Rearranging for \( B \)**:
Rearranging the equation to solve for \( B \) gives us:
\[ B = \frac{A}{m} = \frac{MLT^{-2}}{\frac{M}{L}} = \frac{MLT^{-2} \cdot L}{M} = L^2T^{-2} \]

6. **Identifying the Dimensions of \( B \)**:
The dimensional formula we derived for \( B \) is:
\[ [B] = L^2T^{-2} \]

7. **Matching with Given Options**:
We need to identify which of the given options corresponds to the dimensional formula \( L^2T^{-2} \). The options provided are:
- Pressure
- Latent heat
- Work
- None of these

The dimensional formula for latent heat is also \( L^2T^{-2} \), as it is defined as heat per unit mass. Therefore, the correct answer is:
\[ \text{Latent heat} \]

### Final Answer:
The dimensions of \( B \) are of **latent heat**.