Under zero air resistance condition, the sum of potential and kinetic energy of a freely falling body will remain constant.

Potential and Kinetic Energies of a Freely Falling Body

When air resistance is negligible, the sum total of potential and kinetic energies of a freely falling body remains the same.

Explanation:

1. Potential Energy:
Potential energy is the energy possessed by an object due to its position or state. In the case of a freely falling body, the potential energy is gravitational potential energy, which 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
- h is the height of the object above a reference point

As the object falls, its height decreases, resulting in a decrease in potential energy.

2. Kinetic Energy:
Kinetic energy is the energy possessed by an object due to its motion. In the case of a freely falling body, the kinetic energy is given by the formula:

KE = 0.5mv^2

Where:
- KE is the kinetic energy
- m is the mass of the object
- v is the velocity of the object

As the object falls, its velocity increases due to the acceleration due to gravity. Therefore, the kinetic energy increases.

3. Sum Total of Potential and Kinetic Energies:
The sum total of potential and kinetic energies is given by the equation:

Total Energy = Potential Energy + Kinetic Energy

As the object falls, the potential energy decreases, but the kinetic energy increases. However, the decrease in potential energy is exactly equal to the increase in kinetic energy. This means that the sum total of potential and kinetic energies remains constant throughout the fall.

Conclusion:
In the absence of air resistance, the sum total of potential and kinetic energies of a freely falling body remains the same. This is because the decrease in potential energy is exactly balanced by the increase in kinetic energy.