To determine the correct graph showing the relationship between potential energy and the total mass of an object, we need to consider how potential energy (PE) is defined. The gravitational potential energy of an object, for example, is given by the formula:
\[ PE = mgh \]
where:
- \( PE \) is the potential energy,
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (a constant),
- \( h \) is the height above a reference point.
From this formula, we can see that potential energy is directly proportional to the mass of the object, assuming height and gravity remain constant. This means that as mass increases, potential energy will also increase linearly.
So, a graph that correctly depicts this relationship would typically be a straight line that starts from the origin (0,0) and rises linearly as the mass increases.
If you provide the options for the graphs, I can help identify the one that correctly represents this relationship.