A body is falling freely under the action of gravity alone in vacuum. Which one of the following remains constant during the fall?

1. Basics of Gravity and Acceleration (basic)

Welcome to our first step in mastering mechanics! To understand how things move, we must first understand the invisible force that governs everything on Earth: Gravity. At its simplest, gravity is the force of attraction that the Earth exerts on any object. However, in science, we must distinguish between two terms often confused in daily life: Mass and Weight. While mass is the actual "quantity of matter" in an object and remains the same everywhere, weight is the specific force of gravity pulling on that mass (Science, Class VIII NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.142). Because weight depends on gravity, and gravity can vary slightly from place to place, your weight can actually change depending on where you stand!

Gravity isn't perfectly uniform across the globe. It is stronger at the poles and weaker at the equator because the Earth is not a perfect sphere; the equator is further from the Earth's center (Fundamentals of Physical Geography, Geography Class XI NCERT, The Origin and Evolution of the Earth, p.19). Furthermore, the density of materials beneath the surface varies. Scientists call these variations gravity anomalies, and they help us map the distribution of mass within the Earth's crust (Physical Geography by PMF IAS, Earths Interior, p.58). Let’s look at the fundamental differences between mass and weight:

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Force of gravitational attraction.
S.I. Unit	Kilogram (kg).	Newton (N).
Variability	Constant everywhere.	Changes based on location/gravity.

Now, let’s apply this to a moving object. When an object falls freely in a vacuum (meaning no air resistance), it is under the influence of a conservative force: gravity. As it drops, it loses height, which means its Potential Energy decreases. However, gravity causes the object to speed up (accelerate), so its Kinetic Energy increases. According to the Law of Conservation of Mechanical Energy, the sum of these two remains constant throughout the fall. Note a crucial detail for your exams: while energy is conserved, linear momentum is not. Because gravity is an external force acting on the object, its velocity keeps changing, and thus its momentum (mass × velocity) increases as it falls.

Sources: Science, Class VIII NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.142; Fundamentals of Physical Geography, Geography Class XI NCERT, The Origin and Evolution of the Earth, p.19; Physical Geography by PMF IAS, Earths Interior, p.58; Science, Class VIII NCERT, Exploring Forces, p.75

2. Understanding Work, Power, and Energy (basic)

To understand the physical world, we must first master the trio of Work, Energy, and Power. In physics, "work" is not just about effort; it is strictly defined as the product of the force applied to an object and the displacement caused by that force. If you push against a wall and it doesn't move, scientifically speaking, you have done zero work! Energy is the capacity or ability to do this work. It exists in many forms—mechanical, chemical, thermal, and electrical—and is often transformed from one type to another during physical processes Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.14.

When we look at Mechanical Energy, we focus on two primary types: Kinetic Energy (KE), which is the energy an object possesses due to its motion, and Potential Energy (PE), which is the energy stored due to an object's position or height. For instance, a ball held high above the ground has maximum PE. As it falls, its height decreases (reducing PE), but its speed increases (increasing KE). Power, on the other hand, is the rate at which this work is done or energy is transferred. In electrical systems, for example, power is the rate at which a source supplies energy to a circuit Science class X, NCERT 2025 ed., Electricity, p.188.

Concept	Definition	Core Insight
Work	Force applied over a distance (W = F × d).	No movement means no work is done.
Energy	The capacity to perform work.	Total energy in a closed system is conserved.
Power	The rate of doing work (P = W / t).	How fast energy is being consumed or generated.

One of the most fundamental laws you must remember for the UPSC is the Law of Conservation of Mechanical Energy. It states that in the absence of external non-conservative forces (like air resistance or friction), the sum of kinetic and potential energy remains constant. In a vacuum, as a body falls, every joule of potential energy lost is perfectly converted into a joule of kinetic energy. While the individual values of KE and PE change throughout the journey, their total sum—the Mechanical Energy—never wavers.

Sources: Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.14; Science class X, NCERT 2025 ed., Electricity, p.188

3. Newton’s Laws of Motion and Force (intermediate)

Newton’s laws provide the foundation for understanding how objects move and interact. A force—measured in newtons (N)—is a push or pull that changes an object's state of rest or motion Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.65. When an object moves along a straight path, such as a train between stations, it is undergoing linear motion Science-Class VII, NCERT (Revised ed 2025), Measurement of Time and Motion, p.116. In the absence of friction, an object would continue its motion indefinitely; however, in the real world, forces like friction often act to slow things down Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.67.

Consider the specific case of free fall, such as a fruit falling from a tree Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.77. Here, the primary force at work is gravity. According to the Law of Conservation of Mechanical Energy, the total energy (the sum of Potential Energy and Kinetic Energy) of an object remains constant in a vacuum. As the object falls, its height decreases, causing its Gravitational Potential Energy (PE) to drop. Simultaneously, gravity accelerates the object, increasing its velocity and its Kinetic Energy (KE). The loss in PE is exactly balanced by the gain in KE.

Property	Change During Free Fall (Vacuum)	Conservation Status
Potential Energy (PE)	Decreases (Height drops)	Not conserved alone
Kinetic Energy (KE)	Increases (Speed rises)	Not conserved alone
Total Mechanical Energy	Remains Unchanged (PE + KE)	Conserved
Linear Momentum	Increases (Velocity increases)	Not Conserved

It is a common misconception that all physical quantities are conserved during this process. While energy is conserved, total linear momentum is not. Momentum (mass × velocity) changes because an external force—gravity—is acting on the body, causing it to accelerate. For momentum to be conserved, the net external force acting on the system must be zero. Since gravity is constantly pulling the object downward, the object's velocity increases, and thus its momentum increases throughout the fall.

Sources: Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.65; Science-Class VII, NCERT (Revised ed 2025), Measurement of Time and Motion, p.116; Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.67; Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.77

4. Linear Momentum and Impulse (intermediate)

To understand the motion of objects beyond just 'pushing and pulling,' we must look at Linear Momentum. Think of momentum as the 'quantity of motion' an object possesses. It is the product of an object’s mass (m) and its velocity (v), expressed as p = mv. Because velocity is a vector, momentum is also a vector, meaning its direction matters just as much as its magnitude. As we learn in basic physics, a force can change the speed or direction of an object Science, Class VIII NCERT, Exploring Forces, p.64; more specifically, Newton’s Second Law tells us that the net force acting on an object is exactly equal to the rate at which its momentum changes (F = Δp/Δt).

While momentum tells us what an object 'has,' Impulse tells us what a force 'does' over a period of time. When a force acts on an object for a specific duration, it causes a change in the object's momentum. This product of force and time is called Impulse (J = F · Δt). This leads us to the Impulse-Momentum Theorem, which states that the Impulse applied to an object is equal to its change in momentum (J = Δp). This is why contact forces Science, Class VIII NCERT, Exploring Forces, p.66 are so critical in sports or collisions—the duration of that contact determines how much force is felt.

The beauty of this concept lies in its applications to safety and efficiency. If you want to stop a moving object (change its momentum to zero), you have two choices: apply a large force for a short time, or a small force for a long time. This is the scientific reason behind airbags in cars and why cricketers pull their hands back while catching a fast-moving ball. By 'softening' the impact, they increase the time (Δt) of the interaction, which significantly reduces the impact force (F) required to achieve the same change in momentum.

Sources: Science, Class VIII NCERT, Exploring Forces, p.64; Science, Class VIII NCERT, Exploring Forces, p.66

5. Conservative vs. Non-conservative Forces (intermediate)

In our journey through mechanics, we now encounter a pivotal distinction: how forces handle energy. We categorize forces into two types based on whether the energy they "spend" can be recovered. This distinction is the bedrock of the Law of Conservation of Mechanical Energy.

Conservative forces are those where the work done in moving an object between two points is independent of the path taken. Imagine lifting a book from the floor to a table. Whether you lift it straight up or move it in a complex spiral, the work done against gravity depends only on the starting and ending heights. As noted in Science, Class VIII NCERT, Exploring Forces, p.72, when an object is thrown upwards or dropped, it moves under the influence of gravity. In a vacuum, gravity is a conservative force; the Potential Energy (PE) lost as it falls is perfectly converted into Kinetic Energy (KE). The total mechanical energy (PE + KE) remains constant at every point of the flight.

Non-conservative forces, on the other hand, are "path-dependent." The most common examples are friction and air resistance. If you slide a crate across a floor, the longer the path you take, the more work you must do against friction. Unlike gravity, this work isn't "stored" for later use; it is dissipated as heat or sound. When these forces are present, mechanical energy is not conserved—it leaks out of the system. For instance, an air parcel rising or falling in the atmosphere experiences changes in density and temperature, often involving non-adiabatic processes where energy is exchanged with the surroundings Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.298.

Feature	Conservative Force (e.g., Gravity)	Non-conservative Force (e.g., Friction)
Path Dependency	Independent of the path taken.	Dependent on the path taken.
Work in a Closed Loop	Zero (returning to start recovers all energy).	Non-zero (energy is lost as heat).
Energy Conservation	Mechanical energy is conserved.	Mechanical energy is dissipated.

Sources: Science, Class VIII NCERT, Exploring Forces, p.72; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.298

6. Dynamics of Potential and Kinetic Energy (intermediate)

To understand the dynamics of energy, we must first look at the Law of Conservation of Mechanical Energy. In a system where only conservative forces—like gravity—are acting, the total mechanical energy (the sum of Kinetic Energy and Potential Energy) remains constant. Kinetic energy is the energy an object possesses due to its motion, while potential energy is 'stored' energy based on its position or configuration. For instance, wind turbines demonstrate this by capturing the kinetic energy of moving air and converting it into mechanical power Environment, Shankar IAS Academy, Renewable Energy, p.290.

Let’s visualize a body in free fall within a vacuum. At the highest point, the body has maximum gravitational potential energy (PE = mgh) and zero kinetic energy (KE = ½mv²). As it begins to fall, its height (h) decreases, causing its potential energy to drop. However, because gravity is an external force accelerating the object, its velocity (v) increases. This acceleration transforms the lost potential energy directly into kinetic energy. While the individual values of PE and KE change at every millisecond of the descent, their sum stays exactly the same. This is distinct from linear momentum, which does not remain constant during free fall because the force of gravity is continuously changing the object's velocity over time.

In the real world, these dynamics are slightly more complex. Factors like air resistance act as non-conservative forces, converting some mechanical energy into heat. Furthermore, the gravitational force itself is not perfectly uniform across the globe. Variations in the mass distribution within the Earth's crust, known as gravity anomalies, mean that the potential energy of an object can vary slightly depending on its precise geographic location Physical Geography by PMF IAS, Earths Interior, p.58. Despite these nuances, the fundamental principle remains: energy is neither created nor destroyed, only transformed from one state to another.

Sources: Environment, Shankar IAS Academy, Renewable Energy, p.290; Physical Geography by PMF IAS, Earths Interior, p.58; Science-Class VII NCERT, Measurement of Time and Motion, p.119

7. Law of Conservation of Mechanical Energy (exam-level)

To understand the Law of Conservation of Mechanical Energy, we must first define what we are conserving. Mechanical Energy is the sum of an object’s Kinetic Energy (energy of motion) and its Potential Energy (stored energy based on position). In physics, a fundamental principle states that if a system is subject only to conservative forces—like gravity—the total mechanical energy remains constant over time. While energy can be transformed from one type to another (similar to how a battery’s chemical energy can be converted to light or mechanical work), the 'total' value in a closed mechanical system does not change Science, class X (NCERT 2025 ed.), Life Processes, p.88.

Consider the example of a debris fall—a nearly free fall of material from a vertical face Physical Geography by PMF IAS, Geomorphic Movements, p.89. At the highest point, the debris has maximum Gravitational Potential Energy (PE = mgh) but zero Kinetic Energy (KE). As it begins to fall, gravity—an external force—causes it to accelerate, changing its speed and motion Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.64. As its height decreases (losing PE), its velocity increases (gaining KE). Crucially, every Joule of potential energy lost is exactly balanced by a Joule of kinetic energy gained. Thus, PE + KE = Constant.

However, this conservation only holds perfectly in a vacuum. In the real world, contact forces like friction or air resistance act on moving objects Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.67. These are non-conservative forces; they dissipate mechanical energy by turning it into heat or sound. Therefore, while 'Total Energy' in the universe is always conserved, 'Mechanical Energy' is specifically conserved only when these resistive forces are absent or negligible.

State of Motion	Potential Energy (PE)	Kinetic Energy (KE)	Total Mechanical Energy
At Maximum Height	Maximum	Zero	PE + 0
During Descent	Decreasing	Increasing	Constant (Sum of PE + KE)
Just before Impact	Minimum (Zero)	Maximum	0 + KE

Sources: Science, class X (NCERT 2025 ed.), Life Processes, p.88; Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.64, 67; Physical Geography by PMF IAS, Geomorphic Movements, p.89

8. Solving the Original PYQ (exam-level)

Now that you have mastered the building blocks of gravitational potential energy and kinetic energy, this question serves as the ultimate test of the Law of Conservation of Mechanical Energy. In your previous modules, you learned that when an object is positioned at a height, it possesses potential energy, which transforms into kinetic energy as it accelerates downward. The specific mention of a vacuum is your most important clue; it signals that there are no non-conservative forces, such as air resistance, to dissipate energy as heat. This creates an idealized system where the principles discussed in NCERT Class 9 Science apply perfectly.

To arrive at the correct answer, (D) Total mechanical energy, you must visualize the energy balance sheet. As the body falls, its height above the ground decreases, which means its potential energy ($mgh$) is constantly dropping. Simultaneously, the constant pull of gravity causes the body to accelerate, meaning its velocity—and consequently its kinetic energy—is increasing. Because there is no friction to "steal" energy from the system, the loss in potential energy is exactly offset by the gain in kinetic energy. This ensures the sum of the two remains constant throughout the entire fall.

UPSC often includes distractors like Total linear momentum to catch students who confuse energy conservation with momentum conservation. Since gravity acts as an external force, it continuously changes the body's velocity, meaning linear momentum ($p = mv$) cannot be constant. Similarly, options (A) and (B) are incorrect because they represent individual components that are constantly changing into one another. The trap lies in the movement; while the individual types of energy are in flux, the Total mechanical energy is the only quantity that remains invariant in a vacuum.