Explanation:

Introduction:
Energy is required to perform any activity. The amount of energy needed varies depending on the intensity and duration of the activity. In this question, we are given four activities and we need to determine which one requires the most energy.

Analysis:
Let's analyze each activity to determine the amount of energy required:

a) Riding a bicycle up a hill:
When riding a bicycle uphill, the cyclist needs to overcome the force of gravity in addition to the frictional forces acting against the motion. This requires the most amount of energy as the cyclist has to pedal harder and continuously to overcome these forces and move against the incline.

b) Walking:
Walking is a low-intensity activity that requires less energy compared to cycling uphill. Although walking does require some effort, it is not as physically demanding as cycling uphill.

c) Riding a bicycle on a level ground:
Cycling on a level ground is less physically demanding compared to cycling uphill. The cyclist does not have to work against the force of gravity, but there is still some frictional resistance to overcome. Therefore, it requires less energy compared to cycling uphill.

d) Doing homework:
Doing homework is a mental activity that does not require significant physical exertion. While it may require concentration and mental effort, it does not directly consume a large amount of physical energy.

Conclusion:
Based on the analysis, it can be concluded that riding a bicycle up a hill requires the most energy among the given activities. This is because it involves overcoming the force of gravity and frictional forces, which require significant physical exertion.