Which of these is equivalent to 1 Pa?

Options

A. 1 N of force acting over an area of `1m^(3)`
B. 1 N of force acting over an area of `1cm^(2)`
C. 10 N of force acting over an area of `10m^(2)`
D. 100 N of force acting over an area of `100km^(2)`

Answer

To determine which of the options is equivalent to 1 Pascal (Pa), we first need to understand the definition of pressure and the units involved.

### Step-by-Step Solution:

1. **Understand the Definition of Pascal**:
- Pascal (Pa) is the SI unit of pressure.
- Pressure is defined as the force applied per unit area.

2. **Identify the Units**:
- The SI unit of force is Newton (N).
- The SI unit of area is square meter (m²).
- Therefore, 1 Pascal is defined as 1 Newton per square meter (1 Pa = 1 N/m²).

3. **Analyze Each Option**:
- **Option 1**: 1 Newton of force acting over an area of 1 meter cube (m³).
- This option is incorrect because area should be in square meters (m²), not cubic meters (m³).
- **Option 2**: 1 Newton of force acting on an area of 1 cm².
- This option is incorrect because 1 cm² is a CGS unit, not an SI unit. We need to convert it to m² for comparison.
- **Option 3**: 10 Newtons of force acting on an area of 10 m².
- Calculate pressure:
\[ \text{Pressure} = \frac{10 \, \text{N}}{10 \, \text{m}^2} = 1 \, \text{N/m}^2 = 1 \, \text{Pa} \]
- This option is correct.
- **Option 4**: 100 Newtons of force acting over an area of 100 km².
- This option is incorrect because 100 km² needs to be converted to m². Since 1 km = 1000 m, 100 km² = 100,000,000 m², which would yield a very small pressure value.

4. **Conclusion**:
- The correct answer is **Option 3**: 10 N of force acting on an area of 10 m² is equivalent to 1 Pascal.