For a body falling freely under gravity near the Earth's surface, the rate of change of its linear momentum is equal to which physical quantity?

Introduction / Context:
This question connects Newton's second law with the motion of a freely falling body. It asks you to interpret the rate of change of linear momentum in terms of familiar physical quantities like weight, kinetic energy and impulse. Understanding how force, momentum and gravitational acceleration are related is fundamental to classical mechanics and is often tested in objective exams.

Given Data / Assumptions:

• A body is falling freely under gravity near the Earth's surface.
• Air resistance is neglected, so gravity is the only significant force acting on the body.
• The body has mass m and experiences gravitational acceleration g.
• We are interested in the rate of change of linear momentum dp/dt.

Concept / Approach:
Newton's second law states that the net force acting on a body equals the rate of change of linear momentum: F = dp/dt. For a freely falling body, the only force acting is its weight, which is equal to m * g and directed downward. Therefore, the net force F is exactly the weight. Substituting in the law, we get dp/dt = m * g, which is simply the weight of the body. Kinetic energy and potential energy are forms of energy, not forces, and impulse is the change in momentum over a time interval, not the instantaneous rate.

Step-by-Step Solution:
Step 1: Write Newton's second law in its general form: F = dp/dt, where p is linear momentum.Step 2: For a freely falling body, the only significant force is gravitational force (weight) equal to m * g.Step 3: Therefore, the net force F on the body is its weight.Step 4: Equate F and dp/dt to obtain dp/dt = m * g.Step 5: Recognise that m * g is precisely the weight of the body.Step 6: Conclude that the rate of change of linear momentum of the falling body is equal to its weight.

Verification / Alternative check:
You can also reason dimensionally. Momentum has dimensions of mass × velocity, and the rate of change of momentum has dimensions of mass × acceleration, the same as force. Weight is a specific force due to gravity. Kinetic energy and potential energy have dimensions of energy, not force, and impulse has dimensions of momentum, not rate of change of momentum. This dimensional analysis supports the conclusion that dp/dt corresponds to a force, which in this case is the weight.

Why Other Options Are Wrong:
Kinetic energy is 0.5 * m * v^2 and changes as the body falls, but it is not equal to dp/dt; it measures the energy of motion, not the instantaneous force. Potential energy m * g * h is also energy and decreases as the body falls, again not equal to dp/dt. Impulse is defined as the change in momentum over a finite time interval, equal to F * Δt, whereas dp/dt is the instantaneous rate and equals force itself, not impulse.

Common Pitfalls:
Students sometimes confuse related but distinct concepts: energy, force, momentum and impulse. Another common error is to think in terms of scalar energy quantities rather than the vector nature of force and momentum. To avoid such mistakes, always return to the core statement of Newton's second law, F = dp/dt, and identify the actual net force acting on the body. For free fall near the Earth, that force is simply the weight m * g.

Final Answer:
For a freely falling body, the rate of change of its linear momentum is equal to its weight.