The unit kg `m^(2)s^(-2)` is associated wit

Options

A. work only
B. kinetic energy only
C. potential energy only
D. all the above

Answer

To solve the question regarding the unit \( \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} \), we need to analyze the units associated with work, kinetic energy, and potential energy.

### Step-by-Step Solution:

1. **Understanding Work**:
- Work is defined as the product of force and displacement.
- The formula for work is given by:
\[ \text{Work} = \text{Force} \times \text{Displacement} \]
- The unit of force (Newton) is derived from mass and acceleration:
\[ \text{Force} = \text{mass} \times \text{acceleration} = \text{kg} \cdot \text{m/s}^2 \]
- Therefore, the unit of work can be expressed as:
\[ \text{Work} = \text{Force} \times \text{Displacement} = (\text{kg} \cdot \text{m/s}^2) \times \text{m} = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} \]

2. **Understanding Kinetic Energy**:
- Kinetic energy is given by the formula:
\[ \text{Kinetic Energy} = \frac{1}{2} m v^2 \]
- Here, \( m \) is mass and \( v \) is velocity. The unit of velocity is \( \text{m/s} \).
- Thus, the unit of kinetic energy can be calculated as:
\[ \text{Kinetic Energy} = \text{kg} \cdot \left(\frac{\text{m}}{\text{s}}\right)^2 = \text{kg} \cdot \frac{\text{m}^2}{\text{s}^2} = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} \]

3. **Understanding Potential Energy**:
- Potential energy in the context of gravitational potential energy can be expressed as:
\[ \text{Potential Energy} = \text{Force} \times \text{Height} = \text{Weight} \times \text{Height} \]
- The weight is given by \( \text{mass} \times \text{gravity} \):
\[ \text{Weight} = m \cdot g = \text{kg} \cdot \text{m/s}^2 \]
- Therefore, the unit of potential energy is:
\[ \text{Potential Energy} = \text{Weight} \times \text{Height} = (\text{kg} \cdot \text{m/s}^2) \times \text{m} = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} \]

4. **Conclusion**:
- Since all three quantities (work, kinetic energy, and potential energy) share the same unit \( \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} \), we conclude that the correct answer is:
\[ \text{All of the above} \]