Which of the following statements is/are correct for a freely falling body? I. the total is entirely kinetic…

Analysis of the Question

This question tests your understanding of the Law of Conservation of Mechanical Energy as it applies to a body in free fall (ignoring air resistance). We need to evaluate three statements regarding the energy transformations of a falling object.

Concept Explanation

When an object falls freely under gravity:

1. Potential Energy (PE): As the object falls, its height ($h$) decreases, so its potential energy ($PE = mgh$) decreases.
2. Kinetic Energy (KE): As the object falls, its velocity ($v$) increases, so its kinetic energy ($KE = \frac{1}{2}mv^2$) increases.
3. Total Mechanical Energy (TME): According to the Law of Conservation of Energy, the total mechanical energy ($TME = PE + KE$) remains constant throughout the fall, provided there is no air resistance.

Step-by-Step Evaluation

• Statement I: "The total is entirely kinetic." This is incorrect. At the start of the fall, the body has maximum potential energy and zero kinetic energy. During the fall, it has a combination of both. It only becomes "entirely kinetic" at the very instant it hits the ground. Therefore, this statement is not true for the entire duration of the fall.

• Statement II: "The ratio of potential energy to kinetic energy is constant." This is incorrect. Since $PE$ is decreasing and $KE$ is increasing, the ratio $\frac{PE}{KE}$ is constantly changing as the object falls.

• Statement III: "The sum of potential and kinetic energy is constant." This is correct. This is the definition of the Principle of Conservation of Mechanical Energy. As $PE$ is lost, an equal amount of $KE$ is gained, keeping the total sum constant.

Conclusion

Since only Statement III is correct, the correct option is C.

Exam Tip: Whenever you see questions about "freely falling bodies" in JAMB Physics, always remember that Total Energy is conserved. If the question mentions air resistance, the total mechanical energy would decrease because some energy is converted into heat, but in standard JAMB problems, we assume a vacuum unless stated otherwise.