Answer :
Answer:
The graph of gravitational potential energy (GPE) versus height typically shows a linear relationship. Here’s a detailed description and explanation:
### Shape of the Graph
1. **Linear Relationship**:
- The graph is a straight line.
- It slopes upwards from left to right.
2. **Specific Characteristics**:
- As height increases, gravitational potential energy also increases.
- The graph is not curved or parabolic; it is a straight line.
### Explanation of the Relationship between Height and Gravitational Potential Energy
1. **Gravitational Potential Energy (GPE)**:
- GPE is the energy possessed by an object due to its position relative to a reference point, often the Earth’s surface.
- It depends on the height of the object above the reference point.
2. **Mathematical Relationship**:
- Gravitational Potential Energy is given by the formula \( \text{GPE} = mgh \), where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately constant near the Earth’s surface),
- \( h \) is the height of the object above the reference point.
3. **Linear Relationship Explanation**:
- The formula \( \text{GPE} = mgh \) shows that gravitational potential energy is directly proportional to height \( h \) when \( m \) and \( g \) are constant.
- This means that as height increases, gravitational potential energy increases proportionally.
- Therefore, the graph of GPE versus height is a straight line with a positive slope.
### Conclusion
The linear shape of the graph of gravitational potential energy versus height indicates a direct and proportional relationship between height and gravitational potential energy. As height increases, the gravitational potential energy of an object also increases. This relationship is fundamental in understanding how potential energy changes with height in gravitational fields, such as near the Earth’s surface.
