Which one of the following statements is not correct?

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

Hello! Let’s start our journey into mechanics with one of the most elegant laws in physics. Newton’s Universal Law of Gravitation tells us that gravity isn’t just something that happens on Earth—it is a cosmic glue that acts between every single object in the universe. Whether it is a pen falling to the floor or the Earth orbiting the Sun, the same fundamental rule applies. This discovery by Isaac Newton is considered the climax of the scientific revolution, bridging the gap between earthly events and celestial movements Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119.

At its heart, the law states that the gravitational force (F) between two objects depends on two things: their masses and the distance between them. The formula is expressed as F = G(m₁m₂ / r²), where m₁ and m₂ are the masses of the objects, r is the distance between their centers, and G is the Universal Gravitational Constant. From this, we can derive two critical rules:

• Directly proportional to mass: The heavier the objects, the stronger the pull. If you double the mass of one object, the force doubles.
• Inversely proportional to the square of distance: This is the "Inverse Square Law." If you double the distance between two objects, the gravitational pull doesn't just halve—it drops to one-fourth (1/2²) of its original strength.

A common point of confusion in competitive exams is the difference between mass and weight. While we use them interchangeably in daily life, scientifically they are very different. Mass is the actual amount of matter in an object and remains constant no matter where you go in the universe. Weight, however, is a force—specifically, the pull of gravity on that mass. Because weight is a force, its SI unit is the newton (N) Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.65. Your mass would be the same on the Moon as on Earth, but your weight would be much less because the Moon has less mass and thus a weaker gravitational pull Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.75.

In modern science, our understanding of gravity has evolved. While Newton described the force, Einstein’s General Relativity views gravity as the warping of space-time. This has led to the discovery of gravitational waves—ripples in space-time caused by massive objects like black holes. Scientists now use these waves as "sirens" to calculate the distance of stars and the expansion rate of our universe Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.), The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.5-6.

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.75; Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.), The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.5-6

2. Acceleration Due to Gravity (g) (basic)

When we talk about Acceleration due to Gravity (g), we are essentially describing how fast an object speeds up as it falls toward a planet. While gravity is the force that pulls you down, g is the rate at which your velocity increases because of that pull. On Earth, this average value is approximately 9.8 m/s², meaning for every second an object falls, it gains about 9.8 meters per second in speed.

One of the most critical distinctions you must master for the UPSC is the difference between Mass and Weight. Mass is an intrinsic property—the actual amount of matter in your body—and it never changes, whether you are on Earth, the Moon, or floating in deep space. Weight, however, is a force (Mass × g). Because g can change depending on where you are, your weight can change too. Science, Class VIII, NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.75

Does g remain the same everywhere on Earth? Surprisingly, no. Earth is not a perfect sphere; it is an "oblate spheroid," meaning it bulges at the equator and is flattened at the poles. Since gravity gets weaker as you move further from the center of the Earth, g is greater at the poles (closer to the center) and less at the equator (further from the center). Fundamentals of Physical Geography, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19

Furthermore, the value of gravity is influenced by the density of the material beneath your feet. An area with very dense metallic ores will exert a slightly stronger pull than an area with less dense rock. This difference between the actual measured gravity and the expected value is known as a Gravity Anomaly, which geologists use to map the Earth's internal structure. Physical Geography by PMF IAS, Earths Interior, p.58

Sources: Science, Class VIII, NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.75; Fundamentals of Physical Geography, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19; Physical Geography by PMF IAS, Earths Interior, p.58

3. Mass vs. Weight: Fundamental Differences (basic)

In our daily lives, we often use the words mass and weight as if they mean the same thing. However, in the world of physics—and for your UPSC preparation—distinguishing between them is crucial. Mass is an intrinsic property of an object; it represents the actual quantity of matter present within it Science, Class VIII, Chapter 9, p. 142. Whether you are standing on Earth, floating in the International Space Station, or walking on the Moon, your mass remains exactly the same because the amount of "stuff" you are made of hasn't changed.

Weight, on the other hand, is not an intrinsic property but a force. Specifically, it is the gravitational pull exerted on an object by a large body like the Earth Science, Class VIII, Chapter 5, p. 75. Because weight depends on gravity, it changes depending on where you are. For instance, because the Moon’s gravity is much weaker than Earth’s, a 1 kg block that weighs about 9.8 Newtons (N) on Earth would weigh only about 1.6 N on the Moon Science, Class VIII, Chapter 5, p. 75. Even on Earth, your weight can fluctuate slightly depending on your altitude or the density of the ground beneath you, whereas your mass stays constant Science, Class VIII, Chapter 5, p. 77.

The confusion often stems from how we measure things. In everyday language, we say a bag of flour "weighs 10 kg," but kilograms (kg) are actually units of mass Science, Class VIII, Chapter 9, p. 142. Even when calculating the Body Mass Index (BMI) in health studies, we use "weight" measured in kilograms Understanding Economic Development, Class X, Chapter 1, p. 12. Most digital scales actually measure the downward force (weight) but are calibrated to display the result in mass units (kg) for our convenience. In science, we must remember that weight is measured in Newtons (N).

Sources: Science, Class VIII, Exploring Forces, p.75; Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.142; Understanding Economic Development, Class X, DEVELOPMENT, p.12; Science, Class VIII, Exploring Forces, p.77

4. Gravity on Other Celestial Bodies (intermediate)

To master the concept of gravity across the universe, we must first distinguish between two terms often confused in daily speech: Mass and Weight. Mass is the measure of the actual quantity of matter in an object, measured in kilograms (kg). It is an intrinsic property, meaning it does not change whether you are on Earth, the Moon, or floating in deep space Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.75. Weight, however, is a force — specifically, the gravitational pull exerted on an object by a celestial body. Because it is a force, its SI unit is the Newton (N) Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.72.

The strength of this gravitational pull depends on the mass and size of the celestial body you are standing on. For example, the Sun is so massive that its surface gravity is about 274 m/s², which is roughly 28 times that of Earth. Conversely, the Moon is much smaller and less massive, exerting a pull of only 1.62 m/s², or about one-sixth of Earth's gravity Physical Geography by PMF IAS, The Solar System, p.23. This variation means that while your mass remains constant everywhere, your weight fluctuates wildly depending on your location.

Gravity doesn't just pull objects down; it also governs the relationship between celestial bodies. A fascinating example is Tidal Locking. This occurs when an object's orbital period matches its rotational period due to gravitational interaction. This is why the Moon always shows the same face to Earth — its rotation time and orbital time are both 27.3 days Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.257. Furthermore, the Moon's gravity creates tides in our oceans, a constant reminder of the invisible gravitational tether connecting our worlds Physical Geography by PMF IAS, The Solar System, p.29.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.72, 75; Physical Geography by PMF IAS, The Solar System, p.23, 29; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.257

5. Concept of Apparent Weight and Free Fall (intermediate)

To understand Apparent Weight, we must first distinguish between two concepts often confused in daily life: Mass and Weight. Mass is the intrinsic quantity of matter in an object and remains constant whether you are on Earth, the Moon, or floating in deep space. In contrast, weight is the gravitational force exerted on that mass by a planetary body. While we colloquially say a bag of wheat "weighs 10 kg," scientifically, mass is measured in kilograms (kg) and weight is measured in Newtons (N) Science, Class VIII NCERT, Exploring Forces, p.75. Because weight depends on the local gravitational pull, a 1 kg mass that weighs about 9.8 N on Earth would weigh only about 1.6 N on the Moon Science, Class VIII NCERT, Exploring Forces, p.75.

The sensation of "weight" we feel is actually Apparent Weight. You don't actually feel the force of gravity pulling on every atom of your body; instead, you feel the normal reaction force from the floor pushing up against your feet. If you are standing still, the floor pushes up with a force equal to your true weight (W = mg). However, if the surface you are standing on accelerates (like an elevator speeding up or slowing down), the floor must push harder or softer to change your motion. This change in the reaction force is what we perceive as becoming "heavier" or "lighter."

Free Fall is a special state where the only force acting on an object is gravity Science, Class VIII NCERT, Exploring Forces, p.72. Imagine you are in an elevator and the cable snaps. Both you and the elevator accelerate downward at the same rate (g). Because you are falling at the same speed as the floor, the floor stops pushing up against your feet. Since there is no reaction force, your apparent weight becomes zero. This is the state of weightlessness experienced by astronauts in orbit; they aren't "outside" of gravity, but rather in a state of perpetual free fall around the Earth.

Sources: Science, Class VIII NCERT, Exploring Forces, p.75; Science, Class VIII NCERT, Exploring Forces, p.72; Physical Geography by PMF IAS, Earths Interior, p.58

6. Weightlessness in Orbit and Counter-balanced Forces (exam-level)

To understand weightlessness, we must first distinguish between mass and weight. Mass is the actual quantity of matter in an object—an intrinsic property that remains constant whether you are on Earth, the Moon, or floating in the deep void of space. Weight, however, is a force. It is the measure of the gravitational pull exerted on an object Science, Class VIII, Chapter 5: Exploring Forces, p. 72. While mass is measured in kilograms (kg), weight is measured in Newtons (N). When we stand on a scale, we aren't just feeling gravity; we are feeling the resistance of the floor pushing back against us. This "normal force" is what gives us the sensation of weight.

In orbit, such as on the International Space Station (ISS), astronauts experience weightlessness, but it is a common misconception to think this is because gravity is absent. In fact, at the altitude of the ISS, Earth's gravity is still approximately 90% as strong as it is at the surface! The reason astronauts float is that they are in a state of continuous free-fall. Imagine a satellite moving forward at a very high velocity; as gravity pulls it toward Earth, the Earth’s surface curves away beneath it at the exact same rate. This creates a state where the gravitational pull is effectively counter-balanced by the centrifugal force (the apparent outward force resulting from rapid circular motion) Fundamentals of Physical Geography, Geography Class XI, Movements of Ocean Water, p. 109. Because the spacecraft and the astronaut are falling together at the same rate, there is no floor pushing back against them, resulting in the sensation of having zero weight.

This unique environment has significant effects on the human body. During his 1984 mission to the Salyut 7 space station, Indian cosmonaut Rakesh Sharma performed specialized yoga exercises specifically to study how the body adapts to this lack of gravity-induced pressure A Brief History of Modern India, After Nehru, p. 715. Without the constant tug of weight, fluids shift toward the head, and muscles can atrophy, which is why understanding the mechanics of counter-balanced forces is vital for long-term space exploration.

Sources: Science, Class VIII (NCERT 2025), Exploring Forces, p.72; Fundamentals of Physical Geography, Geography Class XI (NCERT 2025), Movements of Ocean Water, p.109; A Brief History of Modern India (Spectrum), After Nehru, p.715

7. Solving the Original PYQ (exam-level)

Now that you have mastered the building blocks of gravitational force and inertia, this question tests your ability to distinguish between an object's intrinsic properties and its interaction with a gravitational field. The core concept here is the formula W = m × g. While mass is a constant measure of matter, weight is the force exerted by gravity. To solve this, you must look past the technical-sounding locations like 'sea level' and focus on the fundamental units: mass is measured in kilograms, while weight is a force measured in Newtons. According to Science, Class VIII, NCERT (Revised ed 2025), these two can never be 'equal' because they represent different physical dimensions.

Walking through the options, we identify that (D) Weight and mass of a body are equal at sea level on the surface of the earth is the incorrect statement and thus our correct answer. Even at sea level, where the gravitational acceleration (g) is approximately 9.8 m/s², a 1 kg mass would have a weight of 9.8 Newtons. The UPSC often uses 'sea level' or 'the poles' as contextual distractors to make a statement seem like a precise scientific law, but no change in location can make a mass (kg) numerically or conceptually equal to a force (N).

The other options serve as a refresher on the behavior of these variables. Statement (A) and (B) correctly highlight that while mass remains identical in empty space or on another planet, weight fluctuates based on the local gravitational field. Statement (C) touches upon the concept of weightlessness, which occurs when the supporting normal force vanishes—such as in free-fall or when gravity is counter-balanced in orbit—as explained in Science, Class VIII, NCERT (Revised ed 2025). Always remember: mass is what you are, and weight is what you feel due to gravity.