For bodies freely falling under gravity near the Earth at a given place (neglecting air resistance), which of the following physical quantities remains constant during the fall?

Introduction / Context:
This question examines your understanding of motion under gravity. When an object falls freely near the Earth surface, its motion is influenced by the gravitational field. Some quantities change during the fall, while others remain constant. Being able to identify the constant acceleration due to gravity g and distinguish it from changing energy values is fundamental in kinematics and energy conservation problems.

Given Data / Assumptions:

• A body is falling freely under gravity near the Earth at a fixed location.
• Air resistance is neglected.
• We consider kinetic energy, potential energy and acceleration as the body falls.
• The local value of gravitational acceleration g is taken as constant.

Concept / Approach:
For free fall near the Earth surface, the acceleration due to gravity g is approximately constant at that location, independent of the mass of the body and its instantaneous speed. As the body falls, its velocity increases linearly with time, so its kinetic energy, which depends on the square of velocity, increases. At the same time, gravitational potential energy decreases because height decreases. Although the sum of kinetic and potential energies remains constant in the absence of air resistance, the individual values of kinetic and potential energy do not. Therefore, among the given options, acceleration is the quantity that remains constant during the fall.

Step-by-Step Solution:
Step 1: For free fall, write the equation of motion: v = u + g * t, where u is initial velocity, v is velocity at time t and g is acceleration due to gravity. Step 2: Notice that g appears as a constant in this equation, meaning acceleration remains the same throughout the motion. Step 3: Kinetic energy is given by K = (1/2) * m * v^2. As v increases with time, K increases, so kinetic energy is not constant. Step 4: Potential energy is given by U = m * g * h, where h is height above a reference level. As the body falls and h decreases, U decreases, so it is not constant either. Step 5: The sum of K and U remains constant (if air resistance is neglected), but the question asks specifically about the listed quantities, not their sum. Step 6: Conclude that only acceleration remains constant among kinetic energy, potential energy and acceleration.

Verification / Alternative check:
Graphical analysis also supports this conclusion. A velocity versus time graph for free fall is a straight line with slope equal to g, indicating constant acceleration. A kinetic energy versus time graph curves upward because kinetic energy depends on v^2. Potential energy versus height is linear, but since height decreases with time in a nonlinear way during fall, potential energy versus time is not constant. These visualisations confirm that acceleration is constant while the energies change.

Why Other Options Are Wrong:
Kinetic energy does not remain constant because the speed of the falling body increases, causing its kinetic energy to increase. Potential energy decreases as the body loses height, so it is also not constant. All the above is incorrect because both kinetic and potential energies change, leaving only acceleration as constant.

Common Pitfalls:
Some students mix up the idea of constant total mechanical energy with individual energy components. While the total energy K + U is conserved in ideal free fall, kinetic energy and potential energy separately change with time. Another common confusion is to think acceleration decreases as the object speeds up, which is not true in uniform gravitational fields near the Earth surface. Remember: for free fall at a fixed location, g is constant and independent of velocity or mass.

Final Answer:
For bodies falling freely under gravity at a given place, the quantity that remains constant is the acceleration due to gravity.