During free fall of an object :

1. Understanding Energy and Work (basic)

In the study of mechanics, Energy is fundamentally defined as the capacity to do work. It is not a physical substance but a property of objects that can be transferred or converted into different forms. Work, on the other hand, occurs when a force is applied to an object, causing it to move over a distance. Think of energy as the "stored potential" and work as the "action" that consumes or transforms that potential. For instance, when a battery powers a device, chemical energy is converted into electrical energy to perform the work of moving electrons or rotating a fan Science, Class X (NCERT 2025), Electricity, p.188.

Two critical forms of mechanical energy are Potential Energy (PE) and Kinetic Energy (KE). Potential energy is energy held by an object because of its position or state—such as a ball held high above the ground. Kinetic energy is the energy of motion; the faster an object moves, the more kinetic energy it possesses. According to the Law of Conservation of Energy, energy cannot be created or destroyed, only transformed from one form to another Environment and Ecology, Majid Hussain, p.14. In a closed system, the total mechanical energy (PE + KE) remains constant. As an object falls, it loses height (decreasing PE) but gains speed (increasing KE), ensuring the sum of energy is balanced.

To measure how effectively we use this energy, we look at Power. Power is defined as the rate of doing work or the rate at which energy is consumed Science, Class X (NCERT 2025), Electricity, p.191. While work tells us "how much" energy was used, power tells us "how fast" it was used. The standard unit for power is the Watt (W), which represents one Joule of work done per second. Understanding these relationships is vital because it explains everything from how a car engine functions to how energy flows through an ecosystem, where plants capture solar energy and transform it into chemical food energy Science, Class X (NCERT 2025), Our Environment, p.210.

Concept	Simple Definition	Key Unit
Energy	The capacity to perform work.	Joule (J)
Work	Force applied over a distance.	Joule (J)
Power	The speed/rate at which work is done.	Watt (W)

Sources: Science, Class X (NCERT 2025), Electricity, p.188, 191; Environment and Ecology, Majid Hussain, Basic Concepts of Environment and Ecology, p.14; Science, Class X (NCERT 2025), Our Environment, p.210

2. Types of Mechanical Energy (basic)

At its core, Mechanical Energy is the energy possessed by an object due to its motion or its position. It is the 'workhorse' of the physical world, representing the sum of two primary forms: Kinetic Energy (KE) and Potential Energy (PE). While we often think of energy as a single abstract concept, in mechanics, it is this duality of 'energy in action' versus 'energy in storage' that allows us to calculate how machines work and how celestial bodies move.

Kinetic Energy is the energy of motion. Any object that has mass and is moving possesses this energy. As seen in the operation of wind turbines, the moving air (wind) carries kinetic energy which is then captured by blades to perform mechanical work Environment, Shankar IAS Academy, Renewable Energy, p.290. Mathematically, it is expressed as KE = ½mv², meaning that an object’s energy increases significantly as its velocity (v) increases. Even at a molecular level, what we perceive as 'temperature' is actually the measurement of the average kinetic energy of vibrating molecules Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.8.

Potential Energy, on the other hand, is 'stored' energy based on an object's position or state. The most common form in basic mechanics is Gravitational Potential Energy (PE = mgh), which depends on an object's mass (m), the acceleration due to gravity (g), and its height (h) above a reference point. A boulder perched on a cliff has high potential energy because of its position; if it falls, that stored energy is released.

Feature	Kinetic Energy (KE)	Potential Energy (PE)
Definition	Energy due to motion.	Energy due to position or state.
Key Variable	Velocity (Speed).	Height (Position).
Example	A flowing river or a moving car.	Water stored behind a dam.

The beauty of mechanical energy lies in the Law of Conservation of Energy. In an ideal system, these two forms are constantly interchanging. As an object falls, its height decreases (losing PE) but its speed increases (gaining KE). The Total Mechanical Energy remains constant, provided external forces like air resistance are negligible. This principle ensures that the energy lost in one form is exactly balanced by the gain in the other.

Sources: Environment, Shankar IAS Academy, Renewable Energy, p.290; Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.8

3. Newton’s Universal Law of Gravitation (basic)

Imagine gravity as the invisible thread that connects everything in the universe, from the smartphone in your hand to the distant galaxies. Newton’s Universal Law of Gravitation states that every particle of matter in the universe attracts every other particle with a force. This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. In simple terms: the heavier the objects, the stronger the pull; the further apart they are, the weaker the pull becomes.

This law is expressed by the formula: F = G(m₁m₂ / r²), where F is the gravitational force, m₁ and m₂ are the masses of the two objects, r is the distance between them, and G is the Universal Gravitational Constant. Because of the "inverse square" relationship (1/r²), if you double the distance between two objects, the gravitational pull doesn't just halve—it drops to one-fourth of its original strength. This force is what keeps us anchored to the ground and acts as the primary driver for geomorphic processes like erosion and the movement of surface materials from higher to lower levels FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Geomorphic Processes, p.38.

Interestingly, gravity is not perfectly uniform across the Earth's surface. Because the mass of material within the Earth's crust is distributed unevenly, the strength of gravity varies slightly from one location to another. Geologists call these differences gravity anomalies, and they use this data to map the distribution of mass within the Earth's crust Physical Geography by PMF IAS, Earths Interior, p.58. In extreme cases, where mass is concentrated into an incredibly small space (like a singularity), gravity becomes so intense that it can even trap light, creating a black hole Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.7.

Factor	Change	Effect on Gravitational Force
Mass	Increases	Force increases proportionally.
Distance	Increases	Force decreases exponentially (inverse square).

Sources: FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Geomorphic Processes, p.38; Physical Geography by PMF IAS, Earths Interior, p.58; Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.7

4. Power and Energy Efficiency (intermediate)

In our journey through mechanics, we have understood energy as the capacity to do work. However, in the real world—and especially in the context of public policy and administration—we often care more about how fast that work is being done. This is the concept of Power. Formally, power is defined as the rate of doing work or the rate of consumption of energy Science, class X (NCERT 2025 ed.), Electricity, p.191. If an agent does a certain amount of work in a shorter time, we say it has more power. Mathematically, it is expressed as:

Power (P) = Work (W) / Time (t)

The SI unit of power is the watt (W), named after James Watt. One watt is the power of an agent which does work at the rate of 1 joule per second. Because the watt is a relatively small unit, we frequently use kilowatts (kW), where 1 kW = 1000 W. When we look at our electricity bills, we see the term kilowatt-hour (kWh). It is vital to distinguish these: while the kilowatt is a unit of power, the kilowatt-hour is a unit of energy (power multiplied by time). One kWh represents the energy consumed by a 1000W appliance running for one hour, which equals 3.6 × 10⁶ Joules Science, class X (NCERT 2025 ed.), Electricity, p.192.

Connected to power is the concept of Energy Efficiency. In any mechanical or electrical system, not all input energy is converted into "useful" work. Much of it is dissipated, often as heat due to friction or resistance. Efficiency is the ratio of useful output energy to the total input energy. For a civil servant, understanding efficiency is key to subjects like sustainable development; for instance, an LED bulb is more "efficient" than an incandescent bulb because it converts a higher percentage of electrical power into visible light rather than wasted heat.

Concept	Definition	Standard Unit
Energy	The total capacity to do work.	Joule (J)
Power	The rate at which work is done.	Watt (W) or J/s
Efficiency	Ratio of useful output to total input.	Percentage (%)

Sources: Science, class X (NCERT 2025 ed.), Electricity, p.191; Science, class X (NCERT 2025 ed.), Electricity, p.192

5. Laws of Motion and Acceleration (intermediate)

At its heart, Force is a push or pull on an object resulting from its interaction with another object Science, Class VIII, Exploring Forces, p.77. While some forces require physical touch (like friction), others like gravity are non-contact forces that act over a distance. When a net force is applied to an object, it doesn't just move; it accelerates. Acceleration is essentially the rate at which an object's velocity changes. In our daily lives, we rarely see uniform motion (constant speed in a straight line); instead, most motion is non-uniform, where the speed or direction is constantly shifting Science, Class VII, Measurement of Time and Motion, p.117.

Consider the specific case of vertical motion under gravity. When you drop a ball, the Earth's gravitational pull acts as a constant force, causing the ball to speed up as it falls Science, Class VIII, Exploring Forces, p.72. This is a perfect example of energy transformation. At the moment you hold the ball high, it possesses Gravitational Potential Energy (GPE) due to its position. As it falls, its height decreases (reducing GPE), but its velocity increases, which builds up Kinetic Energy (KE). Since KE is proportional to the square of the velocity (v²), even a small increase in speed results in a significant jump in kinetic energy.

The beauty of this system lies in the Law of Conservation of Energy. In an ideal scenario without air resistance, the total mechanical energy (the sum of PE and KE) remains constant. Every bit of potential energy lost as the object descends is precisely converted into kinetic energy. This principle allows us to predict the speed of a falling object simply by knowing the height from which it was dropped.

Position of Object	Potential Energy (PE)	Kinetic Energy (KE)	Total Mechanical Energy
At Maximum Height	Maximum	Zero (at rest)	Constant
During Fall	Decreasing	Increasing	Constant
Just before Impact	Minimum (Zero)	Maximum	Constant

Sources: Science, Class VIII (NCERT), Exploring Forces, p.72, 77; Science, Class VII (NCERT), Measurement of Time and Motion, p.117

6. The Law of Conservation of Energy (exam-level)

At its core, the Law of Conservation of Energy states that energy can neither be created nor destroyed; it can only be transformed from one form to another. In any isolated system, the total amount of energy remains constant. While we often hear about "conserving energy" in an environmental context—such as reducing consumption or switching to non-conventional sources to protect our future Geography of India, Energy Resources, p.31—in physics, this law is a fundamental rule governing every physical interaction in the universe.

In mechanics, we focus primarily on Total Mechanical Energy, which is the sum of an object’s Potential Energy (PE) and Kinetic Energy (KE). Think of a ball held at the top of a building. At that height, it possesses maximum gravitational potential energy (PE = mgh) but zero kinetic energy because it isn't moving. The moment you release it, gravity accelerates it downward. As its height decreases, its PE drops; however, its velocity increases, which causes its KE (½mv²) to rise. This is a perfect trade-off: every joule of potential energy lost is converted into a joule of kinetic energy, ensuring the total sum stays the same throughout the fall, provided we ignore air resistance.

Position of Object	Potential Energy (PE)	Kinetic Energy (KE)	Total Energy (PE + KE)
At rest (Top)	Maximum	Zero	Constant
Mid-way Fall	Decreasing	Increasing	Constant
Just before Impact	Zero (Relative to ground)	Maximum	Constant

It is important to understand that energy transformations are not limited to movement. For instance, in biological systems, the energy released during respiration is used to build ATP (adenosine triphosphate) molecules. This ATP acts as a "battery" or energy currency, which cells later break down to drive muscle contraction or nervous impulses Science, Class X, Life Processes, p.88. Whether it is a falling stone, a car coming to a halt due to friction Science, Class VIII, Exploring Forces, p.67, or a cell performing protein synthesis, the energy is never "lost"—it simply changes its face, often dissipating into the environment as heat.

Sources: Science, Class X (NCERT 2025 ed.), Life Processes, p.88; Geography of India, Majid Husain (McGrawHill 9th ed.), Energy Resources, p.31; Science, Class VIII (NCERT Revised ed 2025), Exploring Forces, p.67

7. Dynamics of Free Fall (exam-level)

In the study of mechanics, Free Fall describes the motion of an object acting solely under the influence of gravity. To understand the dynamics here, we look at the interplay between two forms of energy: Gravitational Potential Energy (PE) and Kinetic Energy (KE). When an object is held at a certain height, it possesses PE, which is essentially energy stored due to its position. The moment it is released, gravity accelerates the object downwards, causing its velocity to increase steadily.

According to the Law of Conservation of Energy, energy cannot be created or destroyed, only transformed. During a free fall (in a vacuum or an environment where air resistance is negligible), the object’s height decreases, leading to a loss of Potential Energy. This "lost" energy doesn't disappear; it is converted entirely into Kinetic Energy as the object gains speed. Mathematically, the sum of these energies—the Total Mechanical Energy—remains constant throughout the descent. As velocity increases, the KE (proportional to the square of velocity) grows at the exact same rate that PE declines.

In our atmosphere, these dynamics are slightly more complex because gravity isn't the only force at play. For instance, while gravity pulls air downwards, the vertical pressure gradient force acts in the opposite direction. Usually, these two forces are nearly balanced, which is why we don't see the entire atmosphere collapsing to the ground or rushing into space Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306. However, when an air parcel becomes cooler and denser than its surroundings, the gravitational pull exceeds the buoyancy, and the parcel begins to descend or "fall" Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.298.

Variable	During Descent (Falling)	Physical Reason
Height	Decreases	Moving toward the reference point (ground).
Potential Energy	Decreases	PE is directly proportional to height (PE = mgh).
Velocity	Increases	Constant acceleration due to gravity (g).
Kinetic Energy	Increases	KE is proportional to velocity squared (KE = ½mv²).

Sources: Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.298

8. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamental definitions of Mechanical Energy, this question brings those building blocks together through the Law of Conservation of Energy. In a free-fall scenario, as discussed in NCERT Class 9 Science, we analyze an isolated system where total energy is conserved. You have learned that Gravitational Potential Energy (PE) is tied to an object's height, while Kinetic Energy (KE) is tied to its motion. This PYQ tests your ability to visualize how energy is transformed rather than lost as an object changes its position in a gravitational field.

To arrive at the correct answer, (B) its potential energy decreases and its kinetic energy increases, walk through the physical descent: as the object falls, its height (h) decreases, which mathematically reduces its PE ($mgh$). Simultaneously, the constant pull of gravity causes the object to accelerate, increasing its velocity ($v$). Since KE is defined as $\frac{1}{2}mv^2$, this increasing velocity directly results in a rise in kinetic energy. The logic is simple: the loss in potential energy is exactly balanced by the gain in kinetic energy, ensuring the total mechanical energy remains constant throughout the motion.

UPSC often uses distractors like options (C) and (D) to test if you understand that energy cannot be created or destroyed in this system; both energies cannot increase or decrease simultaneously without violating the First Law of Thermodynamics. Option (A) is a reversal trap designed to catch students who confuse the direction of motion. When you see "free fall," immediately associate it with losing height (losing PE) and gaining speed (gaining KE). Mastering this inverse relationship is key to solving mechanics questions efficiently on exam day.