Which of the following ratios express pressure?

Options

A. Force/Area
B. Energy/Volume
C. Energy/Area
D. Force/Volume

Explanation

To determine which ratios express pressure, we need to understand the definition of pressure and analyze the given options.

### Step-by-Step Solution:

1. **Define Pressure**:
Pressure (P) is defined as the force (F) applied per unit area (A). Mathematically, it is expressed as:
\[ P = \frac{F}{A} \]
where:
- \( P \) = Pressure
- \( F \) = Force
- \( A \) = Area

2. **Identify Units of Pressure**:
The SI unit of force is Newton (N), which can be expressed as:
\[ 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2 \]
The SI unit of area is square meters (m²). Therefore, the unit of pressure becomes:
\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{\text{N}}{\text{m}^2} = \frac{\text{kg} \cdot \text{m/s}^2}{\text{m}^2} = \frac{\text{kg}}{\text{m} \cdot \text{s}^2} \]

3. **Analyze Each Option**:
- **Option 1: Force by Area**:
\[ \text{Unit} = \frac{F}{A} = \frac{\text{N}}{\text{m}^2} = \frac{\text{kg}}{\text{m} \cdot \text{s}^2} \]
This matches the unit of pressure.

- **Option 2: Energy by Volume**:
The unit of energy (work) is Joules (J), which is:
\[ 1 \, \text{J} = 1 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \]
The unit of volume is cubic meters (m³). Therefore:
\[ \text{Unit} = \frac{\text{Energy}}{\text{Volume}} = \frac{\text{J}}{\text{m}^3} = \frac{\text{kg} \cdot \text{m}^2/\text{s}^2}{\text{m}^3} = \frac{\text{kg}}{\text{m} \cdot \text{s}^2} \]
This also matches the unit of pressure.

- **Option 3: Energy by Area**:
\[ \text{Unit} = \frac{\text{Energy}}{\text{Area}} = \frac{\text{J}}{\text{m}^2} = \frac{\text{kg} \cdot \text{m}^2/\text{s}^2}{\text{m}^2} = \frac{\text{kg}}{\text{s}^2} \]
This does not match the unit of pressure.

- **Option 4: Force by Volume**:
\[ \text{Unit} = \frac{F}{\text{Volume}} = \frac{\text{N}}{\text{m}^3} = \frac{\text{kg} \cdot \text{m/s}^2}{\text{m}^3} = \frac{\text{kg}}{\text{m}^2 \cdot \text{s}^2} \]
This also does not match the unit of pressure.

4. **Conclusion**:
The ratios that express pressure are:
- Force by Area
- Energy by Volume

### Final Answer:
The correct options that express pressure are:
1. Force by Area
2. Energy by Volume