An equal amount of increase in kinetic energy
Explanation
The Law of Conservation of Mechanical Energy. This principle states that in an isolated system subject only to conservative forces (such as gravity) and in the absence of dissipative forces (such as air resistance or friction), the total mechanical energy remains constant.
Detailed Analysis:
- Components of Mechanical Energy: The total mechanical energy ($E$) of a body is the sum of its Gravitational Potential Energy ($PE$) and Kinetic Energy ($KE$). Mathematically, $E = PE + KE = \text{constant}$.
- Dynamics of Free Fall: As a body falls freely:
- Its vertical height decreases, leading to a loss in Gravitational Potential Energy ($PE = mgh$).
- Simultaneously, its velocity increases due to the acceleration due to gravity, leading to a corresponding increase in Kinetic Energy ($KE = \frac{1}{2}mv^2$).
- Energy Transformation: Because energy cannot be created or destroyed in this closed system, the energy lost in the form of potential energy is strictly transformed into kinetic energy. Consequently, the magnitude of the loss in potential energy equals the magnitude of the gain in kinetic energy.
- Incorrect Options:
- Heat energy & Sound energy: Transformation into heat or sound energy occurs primarily due to friction or air resistance. The question explicitly specifies the "absence of air resistance."
- An equal amount of decrease in kinetic energy: Kinetic energy increases as the body accelerates downwards; it does not decrease.
Key Takeaway:
In the absence of non-conservative forces like air resistance, the mechanical energy of a falling body is conserved; any decrease in potential energy results in an exactly equal increase in kinetic energy.