When an object is in free fall near the Earth's surface, which of the following physical quantities remains constant if air resistance is neglected?

The correct option is Acceleration due to gravity remains constant.

Step-by-Step Explanation:

When an object is in free fall near the Earth's surface, it moves under the sole influence of gravity, and any air resistance is neglected. To understand why its acceleration remains constant, we can apply Newton's laws of motion.

According to Newton's second law of motion, the net force acting on an object is equal to the product of its mass and its acceleration:
$$F=m\cdot a$$

The gravitational force ($F_g$) acting on an object of mass $m$ near the Earth's surface is given by:
$$F_g=m\cdot g$$
where $g$ represents the acceleration due to gravity.

Since gravity is the only force acting on the object in free fall, we can set the net force equal to the gravitational force:
$$m\cdot a=m\cdot g$$

Dividing both sides of the equation by the mass $m$ gives:
$$a=g$$

Near the surface of the Earth, the value of the acceleration due to gravity ($g$) is approximately constant at $9.8{\text{m/s}}^2$ pointing downwards towards the center of the Earth. Therefore, the acceleration of the falling object remains constant throughout its motion.

Let's examine why the other choices do not remain constant:
1. Velocity: As the object falls, gravity causes it to continuously speed up. Since its speed increases, its velocity is constantly changing and is not constant.
2. Momentum: Momentum is defined as the product of mass and velocity ($p=m\cdot v$). Because the velocity changes, the momentum of the object also changes over time.
3. Energy: Although the total mechanical energy of the system is conserved (remains constant) when air resistance is neglected, the individual forms of energy (kinetic energy and potential energy) are continuously transforming into one another and are not individually constant.