Which of the following pairs have the same SI units?

Options

A. Force and pressure
B. Force and distance
C. Work and energy
D. Momentum and force

Answer

To determine which pairs have the same SI units, we first need to identify the SI units of the quantities mentioned: pressure, force, and momentum.

1. **Identify the SI units:**
- **Pressure**: The SI unit of pressure is Pascal (Pa).
- **Force**: The SI unit of force is Newton (N).
- **Momentum**: The SI unit of momentum is kilogram meter per second (kg·m/s).

2. **Convert the units to their base SI units:**
- **Pascal (Pa)**: 1 Pascal is defined as 1 Newton per square meter (N/m²). Since 1 Newton is 1 kg·m/s², we can express Pascal as:
\[ 1 \text{ Pa} = 1 \text{ N/m}^2 = 1 \text{ (kg·m/s²)}/\text{m}^2 = 1 \text{ kg/(m·s²)} \]
- **Newton (N)**: As mentioned, 1 Newton is 1 kg·m/s².
- **Momentum (kg·m/s)**: The SI unit for momentum is already expressed as kg·m/s.

3. **Compare the units:**
- **Pressure (Pa)**: kg/(m·s²)
- **Force (N)**: kg·m/s²
- **Momentum (kg·m/s)**: kg·m/s

4. **Identify pairs with the same SI units:**
- Comparing the units:
- Pressure (Pa) = kg/(m·s²)
- Force (N) = kg·m/s²
- Momentum (kg·m/s) = kg·m/s

From the comparison, we can see that:
- Pressure and Force do not have the same units.
- Pressure and Momentum do not have the same units.
- Force and Momentum do not have the same units.

5. **Conclusion:**
None of the pairs (Pressure, Force, Momentum) have the same SI units.