Which one of the following statements is correct for a body falling freely under gravity? (neglect air resistance)

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

Imagine you are sitting under a tree, and an apple falls. While this story about Sir Isaac Newton might be a bit of a legend, the logic he derived from it changed science forever. At its heart, Newton’s Universal Law of Gravitation states that every single object in the universe that has mass exerts a pull on every other object with mass. This isn't just a force that exists on Earth; it is universal, meaning it governs the movement of an apple falling to the ground just as much as it governs the Moon orbiting the Earth or planets orbiting the Sun Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119.

Newton quantified this "pull" through a simple but profound relationship. The gravitational force (F) between two objects depends on two primary factors: mass and distance. Specifically, the force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between their centers. We express this as:

F = G (m₁m₂ / r²)

Where G is the Universal Gravitational Constant, m₁ and m₂ are the masses of the two objects, and r is the distance between them. Because the force is measured in Newtons (N) Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.65, even a small change in distance (r) has a massive impact on the force because it is squared in the denominator. This is known as the Inverse Square Law.

Unlike magnetic or electrostatic forces, which can push things away (repel) or pull them in (attract), gravitational force is always an attractive force Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.72. It is also a non-contact force, meaning it acts across empty space without the objects needing to touch. Interestingly, the Earth's pull isn't perfectly uniform everywhere. Because the mass inside the Earth is distributed unevenly, the strength of gravity varies slightly from place to place—a phenomenon scientists call a gravity anomaly Physical Geography by PMF IAS, Earths Interior, p.58.

Factor	Relationship to Force	Effect
Mass	Directly Proportional	If mass increases, the gravitational pull increases.
Distance	Inversely Proportional (Squared)	If distance increases, the gravitational pull decreases rapidly.

Sources: Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119; Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.65; Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.72; Physical Geography by PMF IAS, Earths Interior, p.58

2. Mass, Weight, and Acceleration due to Gravity (basic)

To understand mechanics, we must first distinguish between what an object is and how it is pulled. Mass is the intrinsic quantity of matter within an object. It is a fundamental property that remains constant regardless of where you are in the universe Science, Class VIII, NCERT, Exploring Forces, p.75. Whether you are on the peaks of the Karakoram or in the vacuum of space, your mass does not change. In the SI system, we measure mass in kilograms (kg) Science, Class VIII, NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.142.

Weight, however, is a force. It is the gravitational pull exerted on an object by a planet or moon. Because weight is a force, it is measured in Newtons (N). The relationship is defined by the formula: Weight = Mass × acceleration due to gravity (g). While your mass is constant, your weight can vary slightly depending on your location on Earth or significantly if you move to another planet Science, Class VIII, NCERT, Exploring Forces, p.75. For instance, a spring balance measures this gravitational pull (weight), even if the scale is sometimes calibrated to show mass units for convenience Science, Class VIII, NCERT, Exploring Forces, p.74.

When an object is in free fall in a vacuum, it is influenced only by gravity. In this state, the acceleration due to gravity (g) remains constant (approximately 9.8 m/s² on Earth). This constant acceleration means the object's velocity increases steadily every second. As the object speeds up, its Kinetic Energy (K = ½mv²) increases. Simultaneously, as it loses height, its Gravitational Potential Energy (U = mgh) decreases. Crucially, the Total Mechanical Energy (the sum of kinetic and potential energy) stays the same throughout the fall, illustrating the law of conservation of energy.

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Force of gravity acting on an object.
Constancy	Remains constant everywhere.	Changes based on the local gravity (g).
SI Unit	Kilogram (kg)	Newton (N)
Measurement Tool	Two-pan balance	Spring balance / Weighing scale

Sources: Science, Class VIII, NCERT, Exploring Forces, p.74; Science, Class VIII, NCERT, Exploring Forces, p.75; Science, Class VIII, NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.142

3. Kinetic and Potential Energy Fundamentals (basic)

In our journey through basic mechanics, we encounter the two most fundamental forms of mechanical energy: Kinetic Energy and Potential Energy. At its simplest, energy is the capacity to do work. Kinetic Energy (KE) is the energy an object possesses due to its motion. Whether it is the wind turning a turbine to generate electricity or molecules vibrating to produce sensible heat, the principle remains that movement equates to energy INDIA PEOPLE AND ECONOMY, TEXTBOOK IN GEOGRAPHY FOR CLASS XII (NCERT 2025 ed.), Mineral and Energy Resources, p.61 Environment and Ecology, Majid Hussain (Access publishing 3rd ed.), BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.8. Mathematically, it is expressed as K = ½mv², where 'm' is mass and 'v' is velocity. This means if you double the speed of an object, its kinetic energy actually quadruples!

Potential Energy (PE), on the other hand, is "stored" energy based on an object's position or state. The most common form we study is Gravitational Potential Energy, which depends on an object's height above a reference point and the force of gravity acting upon its mass Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.), Earths Interior, p.58. It is calculated as U = mgh (mass × gravity × height). Think of a stone perched on a cliff: it isn't moving, so its KE is zero, but it has high PE because of its position. If the stone falls, that stored energy is ready to be released.

The beauty of mechanics lies in the Law of Conservation of Energy. In a closed system (ignoring friction or air resistance), energy is neither created nor destroyed; it only changes form. As an object falls, its height decreases (losing PE), but it accelerates due to gravity, meaning its speed increases (gaining KE). The Total Mechanical Energy—the sum of KE and PE—remains constant at every point during the fall.

Feature	Kinetic Energy (KE)	Potential Energy (PE)
Source	Due to motion/velocity.	Due to position/height.
Formula	½mv²	mgh
Example	A flowing river or blowing wind.	Water stored behind a dam.

Sources: INDIA PEOPLE AND ECONOMY, TEXTBOOK IN GEOGRAPHY FOR CLASS XII (NCERT 2025 ed.), Mineral and Energy Resources, p.61; Environment and Ecology, Majid Hussain (Access publishing 3rd ed.), BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.8; Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.), Earths Interior, p.58

4. Escape Velocity and Orbital Motion (intermediate)

To understand how we launch satellites or send probes to Mars, we must first grasp the tug-of-war between gravity and velocity. Imagine throwing a stone upward; it eventually falls back because gravity converts its kinetic energy into potential energy. However, if you throw that stone with enough speed, it can either circle the Earth indefinitely (Orbital Motion) or leave Earth's influence entirely (Escape Velocity).

Escape Velocity is the minimum speed an object must reach to break free from a planet's gravitational pull without further propulsion. For Earth, this is approximately 11.2 km/s. Interestingly, this speed is independent of the mass of the escaping object; whether it’s a tiny speck or a massive rocket, the speed required is the same because it depends solely on the planet's mass and radius. We see this in action with deep-space probes that have successfully achieved escape velocity to leave our Solar System Physical Geography by PMF IAS, The Solar System, p.39.

Orbital Motion, on the other hand, is a delicate balance. If an object travels horizontally at just the right speed (Orbital Velocity), the rate at which it 'falls' toward Earth matches the rate at which the Earth’s surface curves away from it. Most artificial satellites orbit at about 800 km above the surface, completing a revolution in roughly 100 minutes Science, Class VIII. NCERT, Keeping Time with the Skies, p.185. To maintain this motion without slowing down due to friction, satellites are placed in the exosphere, where the air is so thin that atmospheric drag is negligible Physical Geography by PMF IAS, Earths Atmosphere, p.280.

Concept	Objective	Relation to Earth
Orbital Velocity	To stay in a stable circular path around the body.	~7.9 km/s (near surface)
Escape Velocity	To leave the gravitational field completely.	~11.2 km/s

Sources: Physical Geography by PMF IAS, The Solar System, p.39; Science, Class VIII. NCERT, Keeping Time with the Skies, p.185; Physical Geography by PMF IAS, Earths Atmosphere, p.280

5. Weightlessness and Satellite Mechanics (intermediate)

To understand weightlessness, we must first distinguish between mass (the amount of matter) and weight (the force of gravity acting on that mass). In daily life, we 'feel' our weight because the ground pushes back against our feet with an equal and opposite force. However, when an object undergoes vertical motion influenced solely by gravity, it is said to be in free fall. In this state, the speed of the object increases as it descends, but because there is no surface to push back against it, the object experiences weightlessness Science, Class VIII, NCERT, Exploring Forces, p.72. This is exactly what Indian cosmonaut Rakesh Sharma experienced and studied during his 1984 mission aboard the Salyut 7 space station Rajiv Ahir, A Brief History of Modern India, After Nehru, p.715.

Satellite mechanics is essentially an extension of this principle. A satellite in orbit is actually in a state of perpetual free fall. It is moving forward so fast that as it falls toward Earth, the Earth’s surface curves away beneath it. Because the satellite and everything inside it (including astronauts) are accelerating toward Earth at the same rate, there is no relative force between them, creating the sensation of zero gravity. To achieve this delicate balance, India utilizes sophisticated launch vehicles like the PSLV (Polar Satellite Launch Vehicle) and GSLV (Geosynchronous Satellite Launch Vehicle) to provide the exact velocity required to maintain a stable orbit Geography of India, Majid Husain, Transport, Communications and Trade, p.58.

During this orbital motion or free fall, energy transformation is a key feature. As an object falls, its Potential Energy (U = mgh) decreases because its height decreases, while its Kinetic Energy (K = ½mv²) increases because its speed is rising Science, Class VIII, NCERT, Exploring Forces, p.72. Crucially, the Total Mechanical Energy (the sum of potential and kinetic energy) remains constant throughout the flight, illustrating the Law of Conservation of Energy.

Feature	Weight on Earth	Weightlessness in Orbit
Force felt	Gravity + Reaction Force from ground	Gravity only (no reaction force)
Energy state	High Potential Energy (stationary)	Constant exchange of PE and KE
Sensation	Normal weight	Feeling of 'floating'

Sources: Science, Class VIII, NCERT, Exploring Forces, p.72; Rajiv Ahir, A Brief History of Modern India, After Nehru, p.715; Geography of India, Majid Husain, Transport, Communications and Trade, p.58

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

In the study of mechanics, the Law of Conservation of Mechanical Energy is a fundamental principle stating that if only conservative forces (like gravity or spring forces) are doing work on an object, the total mechanical energy of that object remains constant. Mechanical Energy (E) is defined as the sum of an object’s Kinetic Energy (K)—the energy of motion—and its Potential Energy (U)—the energy stored due to its position or configuration.

Consider an object in free fall. As it descends from a height, its height decreases, leading to a reduction in its Gravitational Potential Energy (U = mgh). However, because the object is subject to the constant acceleration of gravity, its velocity increases linearly over time, which in turn increases its Kinetic Energy (K = ½mv²). While the individual forms of energy fluctuate, the sum (K + U) remains identical at every point in the flight. This is much like the concept of energy being a "currency" that can be converted between different forms to drive different processes, a principle seen even in biological systems where energy released in one form is used to power another Science, Class X (NCERT 2025 ed.), Life Processes, p.88.

However, in the real world, we often observe objects slowing down and stopping. For instance, a lunch box pushed across a floor eventually comes to rest due to friction Science, Class VIII, Exploring Forces, p.67. In such cases, mechanical energy is not conserved because friction is a non-conservative force that transforms mechanical energy into heat or sound. It is vital to distinguish between the Conservation of Energy (which is universal and absolute) and the Conservation of Mechanical Energy (which only holds true when dissipative forces like friction or air resistance are absent).

Sources: Science, Class X (NCERT 2025 ed.), Life Processes, p.88; Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.67

7. The Physics of Free Fall (exam-level)

In physics, free fall occurs when an object descends toward the Earth solely under the influence of gravity, with no other forces like air resistance acting upon it. During this descent, the Earth pulls the object with a constant force, leading to a state of vertical linear motion Science-Class VII NCERT, Measurement of Time and Motion, p.116. The most critical point to grasp is that while the object's speed goes on increasing throughout the fall Science, Class VIII NCERT, Exploring Forces, p.72, its acceleration remains constant. This constant acceleration is known as the acceleration due to gravity (denoted as g, approximately 9.8 m/s²). Because the velocity (v) increases linearly over time (v = gt), the object's momentum (p = mv) also increases continuously until it hits the ground.

From an energetics perspective, free fall is a perfect demonstration of the Law of Conservation of Energy. At the moment of release, the object possesses maximum Gravitational Potential Energy (PE = mgh) but zero Kinetic Energy (KE = ½mv²). As it falls, its height (h) decreases, causing the Potential Energy to drop. Simultaneously, its velocity (v) increases, causing the Kinetic Energy to rise. In a vacuum, the loss in Potential Energy is exactly equal to the gain in Kinetic Energy at every point in the flight. This means the Total Mechanical Energy (the sum of PE and KE) remains constant throughout the motion.

This principle isn't just theoretical; it explains real-world phenomena like debris fall, where earth materials drop nearly freely from vertical faces or overhanging cliffs Physical Geography by PMF IAS, Geomorphic Movements, p.89. Whether it is a tiny pebble or a massive rock, the physics of their acceleration remains the same in the absence of air resistance.

Parameter	During Free Fall (Downward)	Reasoning
Acceleration (g)	Constant	Gravity exerts a uniform pull near the Earth's surface.
Velocity (v)	Increasing	Acceleration causes a continuous gain in speed.
Potential Energy	Decreasing	Height above the reference point is reducing.
Kinetic Energy	Increasing	Velocity is squared in the KE formula (KE = ½mv²).
Total Energy	Constant	Energy is transformed from PE to KE, not lost.

Sources: Science-Class VII NCERT, Measurement of Time and Motion, p.116; Science, Class VIII NCERT, Exploring Forces, p.72; Physical Geography by PMF IAS, Geomorphic Movements, p.89

8. Solving the Original PYQ (exam-level)

This question perfectly synthesizes your recent modules on Newtonian mechanics and the law of conservation of energy. To solve it, you must apply the principle that in a closed system neglecting air resistance, the total mechanical energy remains constant. As the body falls, it transitions from a state of high gravitational potential energy (based on height) to high kinetic energy (based on motion). Understanding this energy transformation is the key to unlocking the mechanics of free fall as described in NASA's Guide to Aeronautics.

To arrive at the correct answer, Option (B), follow the path of the falling object: as height ($h$) decreases, the potential energy ($U = mgh$) must decrease. Because the object is subject to the constant acceleration due to gravity ($g$), its velocity ($v$) increases linearly with time. Since kinetic energy ($K = ½mv²$) is tied to the square of that velocity, it must increase. Effectively, the potential energy is being "converted" into kinetic energy throughout the descent, keeping the sum of the two constant.

UPSC often uses common misconceptions as distractors. Option (A) is a classic trap; while the velocity increases, the acceleration remains constant near the Earth's surface. Similarly, Option (D) is incorrect because momentum ($p = mv$) is a product of mass and velocity; since the velocity is increasing, the momentum cannot remain constant. By systematically checking each variable—acceleration, energy, and momentum—you can avoid these conceptual hurdles and focus on the inverse relationship between the two energy types.