Which one among the following statements is not correct ?

1. Fundamentals of Motion: Newton’s Three Laws (basic)

To understand mechanics, we must first understand Force, which is simply a push or a pull on an object resulting from its interaction with another object Science, Class VIII, Chapter 5: Exploring Forces, p.77. In the world of physics, force is the 'agent' of change. It is measured in a unit called the newton (N) Science, Class VIII, Chapter 5: Exploring Forces, p.65. Without force, an object’s state of motion—whether it is sitting still or moving in a straight line at a steady pace—would never change. Newton’s Three Laws provide the framework for how these forces operate. The First Law (Inertia) tells us that objects are 'stubborn'; an object at rest stays at rest, and an object in motion continues in linear motion (moving along a straight line) unless acted upon by an external force Science-Class VII, Measurement of Time and Motion, p.116. The Second Law (F = ma) quantifies this, stating that the force applied to an object is equal to its mass multiplied by its acceleration. Finally, the Third Law reminds us that forces always occur in pairs: for every action, there is an equal and opposite reaction. Forces can be categorized into two main types based on how they interact with objects:

Type of Force	Description	Examples
Contact Forces	Require physical touch between objects.	Muscular force, Frictional force
Non-contact Forces	Act through a space without physical touch.	Magnetic, Electrostatic, and Gravitational forces

Whether it is a train speeding up between stations or a ball being compressed, a force is always responsible for changing an object's speed, its direction of motion, or even its shape Science, Class VIII, Chapter 5: Exploring Forces, p.77.

Sources: Science, Class VIII, Chapter 5: Exploring Forces, p.65; Science, Class VIII, Chapter 5: Exploring Forces, p.77; Science-Class VII, Measurement of Time and Motion, p.116

2. Universal Law of Gravitation (basic)

Newton’s Universal Law of Gravitation states that every particle of matter in the universe attracts every other particle with a force. This force acts along the line joining the centers of the two objects. Crucially, the magnitude of this force is directly proportional to the product of their masses (m₁ and m₂) and inversely proportional to the square of the distance (r) between them. The formula is expressed as: F = G (m₁m₂ / r²), where G is the Universal Gravitational Constant. This law is considered "universal" because it applies to all bodies, whether they are small terrestrial objects or massive celestial bodies like stars and planets NCERT Science Class VIII (Revised ed 2025), Chapter 5, p. 73. It is important to understand that this is an empirical law. This means Sir Isaac Newton formulated it based on observations of the natural world—specifically planetary motion (Kepler’s Laws) and the behavior of falling objects on Earth—rather than deriving it as a logical consequence of his three Laws of Motion. While the Laws of Motion tell us how objects move when a force is applied, the Law of Gravitation defines the specific nature of one such force. Furthermore, we must distinguish between mass (the amount of matter in an object, measured in kg) and weight (the gravitational force acting on that mass, measured in Newtons). Because weight depends on gravity, it can change; for example, at the very center of the Earth, the gravitational pull from the surrounding mass cancels out in all directions, making your weight effectively zero NCERT Science Class VIII (Revised ed 2025), Chapter 5, p. 73. On a larger scale, the gravitational force isn't perfectly uniform across the Earth's surface. Variations in the density of materials within the Earth lead to gravity anomalies. Such anomalies provide vital information about the distribution of mass in the Earth's crust. For instance, in deep oceanic trenches where subduction occurs, there is a localized "loss" of mass, leading to a slightly lower gravitational pull in those specific areas Physical Geography by PMF IAS, Tectonics, p. 108.

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Force of gravity acting on an object.
SI Unit	Kilogram (kg)	Newton (N)
Variability	Constant everywhere.	Changes based on location (e.g., zero at Earth's center).

Sources: Science, Class VIII. NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.73; Physical Geography by PMF IAS, Earths Interior, p.58; Physical Geography by PMF IAS, Tectonics, p.108

3. Kepler’s Laws of Planetary Motion (intermediate)

For centuries, astronomers believed that heavenly bodies moved in perfect circles. Johannes Kepler shattered this notion by proving that planets follow more complex, yet predictable, mathematical paths. His work serves as the bridge between pure observation and the mechanical laws of the universe. While Kepler described how planets move, his laws later provided the empirical foundation for Isaac Newton to explain why they move (gravity) Science, Class VIII NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p. 73.

Kepler’s First Law (The Law of Ellipses) states that the orbit of a planet is an ellipse, with the Sun situated at one of the two "foci" (singular: focus). Because an ellipse is an elongated circle, the distance between the planet and the Sun is constantly changing throughout its revolution Physical Geography by PMF IAS, The Solar System, p. 21.

Kepler’s Second Law (The Law of Equal Areas) describes the planet's speed. It states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. To keep the "area" the same when the planet is far from the Sun, it must move slower; when it is closer, it must move faster to sweep the same amount of space Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p. 257. For Earth, this means our orbital velocity is slowest at the apogee (farthest point) and fastest at the perigee (closest point).

Kepler’s Third Law (The Law of Harmonies) provides a precise mathematical link: the square of the orbital period (T) is proportional to the cube of the semi-major axis (r) of its orbit (T² ∝ r³). Essentially, the further a planet is from the Sun, the significantly longer it takes to complete one orbit, not just because the path is longer, but because it is moving at a slower average speed Physical Geography by PMF IAS, The Solar System, p. 21.

Law	Core Concept	Key Implication
1st Law	Elliptical Orbits	The distance to the Sun is not constant.
2nd Law	Equal Areas	Planets speed up as they get closer to the Sun.
3rd Law	T² ∝ r³	Outer planets have much longer years than inner planets.

Interestingly, these laws affect our calendar. Because Earth is farther from the Sun during the Northern Hemisphere summer, it moves slower in its orbit (Kepler’s Second Law). Consequently, it takes longer to travel from the summer solstice to the autumnal equinox, making summer in the Northern Hemisphere roughly 92 days long, while winter is only about 89 days Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p. 256.

Sources: Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.73; Physical Geography by PMF IAS, The Solar System, p.21; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.256, 257

4. Circular Motion and Satellite Mechanics (intermediate)

To understand how satellites stay in orbit, we must first look at the Universal Law of Gravitation. Newton’s law states that every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them (F = G(m₁m₂)/r²). It is important to realize that this is an empirical law—it was derived from observing planetary motion (Kepler’s Laws) and terrestrial gravity, rather than being a purely logical derivation from Newton’s three laws of motion Science NCERT (Revised 2025), Chapter 5, p.73. Within this framework, we distinguish between Mass (the amount of matter, measured in kg) and Weight (the gravitational force acting on that mass, measured in Newtons). Interestingly, at the very center of the Earth, your weight would be zero because the surrounding mass pulls you equally in every direction, canceling out the net gravitational force Science NCERT (Revised 2025), Chapter 5, p.73.

When we apply gravity to celestial bodies, we look to Kepler’s Laws of Planetary Motion. Kepler noted that orbits are not perfect circles but ellipses, with the Sun at one focus Physical Geography by PMF IAS, The Solar System, p.21. His second law reveals a fascinating dynamic: a planet sweeps out equal areas in equal intervals of time. This means a planet (or satellite) does not move at a constant speed; it moves fastest at the perigee (point closest to the center of gravity) and slowest at the apogee (farthest point) Physical Geography by PMF IAS, The Motions of The Earth, p.257. For a satellite to maintain this curved path, centripetal acceleration must act on it, creating a force directed inward toward the center of rotation Physical Geography by PMF IAS, Pressure Systems and Wind System, p.309.

India’s mastery of these mechanics is evident in our satellite programs. We use the Polar Satellite Launch Vehicle (PSLV) and the Geosynchronous Satellite Launch Vehicle (GSLV) to place satellites like the IRS (Indian Remote Sensing) series into specific orbits INDIA PEOPLE AND ECONOMY NCERT, Transport and Communication, p.84. While the PSLV is the "workhorse" for sun-synchronous polar orbits, the GSLV uses advanced cryogenic stages to reach higher altitudes, despite the technical complexities involved in such missions Geography of India by Majid Husain, Transport, Communications and Trade, p.58.

Concept	Key Characteristic
Mass	Intrinsic property; measured in kilograms (kg).
Weight	A force (mass × gravity); measured in Newtons (N).
Perigee/Perihelion	Closest point in orbit; maximum orbital velocity.
Apogee/Aphelion	Farthest point in orbit; minimum orbital velocity.

Sources: Science NCERT (Revised 2025), Chapter 5: Exploring Forces, p.73; Physical Geography by PMF IAS, The Solar System, p.21; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.257; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.309; INDIA PEOPLE AND ECONOMY NCERT (2025), Transport and Communication, p.84; Geography of India by Majid Husain, Transport, Communications and Trade, p.58

5. Variations in Acceleration due to Gravity (g) (exam-level)

To understand variations in acceleration due to gravity (g), we must first recognize that 'g' is not a universal constant—that title belongs to 'G'. Instead, 'g' is a local variable that depends on how much mass is beneath you and how far you are from the center of that mass. On Earth, this value is roughly 9.8 m/s², but it changes based on where you stand. The most significant variation comes from the Earth's shape: our planet is an oblate spheroid, meaning it bulges at the equator and is flattened at the poles. Because the equatorial radius is greater than the polar radius, you are physically further from Earth's center at the equator. Consequently, gravity is greater near the poles and less at the equator FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), p.19. Beyond just shape, the composition of the Earth's crust plays a role. The Earth is not a uniform ball of billiard-hall material; it has pockets of dense ores and lighter sedimentary rocks. This uneven distribution of mass causes the measured gravity to differ from the mathematically expected value at certain locations. This difference is known as a gravity anomaly, and it provides geologists with vital clues about the materials hidden within the Earth's crust Physical Geography by PMF IAS, Earths Interior, p.58. Finally, we must consider altitude and depth. As you climb a mountain, your distance (r) from the Earth's center increases, causing 'g' to decrease. Interestingly, the opposite happens as you go down: as you descend toward the center of the Earth, the mass of the planet 'above' you begins to pull you upward, counteracting the pull of the mass 'below' you. At the exact center of the Earth, the gravitational pull from all directions cancels out perfectly, resulting in a net acceleration due to gravity of zero. This is why we distinguish between mass (measured in kg), which is constant, and weight (measured in Newtons), which fluctuates as 'g' changes Science, Class VIII, NCERT (Revised ed 2025), p. 73.

Factor	Change in Position	Effect on gravity (g)
Latitude	Moving from Equator to Pole	Increases (distance to center decreases)
Altitude	Increasing height (e.g., Himalayas)	Decreases (distance to center increases)
Mass Distribution	Moving over high-density minerals	Increases (Gravity Anomaly)

Sources: 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; Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.73

6. Physical Quantities: Mass vs. Weight (basic)

In our daily lives, we often use the terms mass and weight as if they mean the same thing. However, in the world of physics, they represent two very different concepts. Mass is a fundamental property of an object; it represents the actual quantity of matter present in that object Science, Class VIII. NCERT (Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.142. Because it is an intrinsic property, your mass does not change whether you are standing on the Earth, orbiting in a space station, or walking on the Moon. Its standard SI unit is the kilogram (kg).

Weight, on the other hand, is not a property of the object itself, but a measure of the gravitational force with which a planet or moon pulls on that object Science, Class VIII. NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.75. Since weight is a force, its SI unit is the newton (N) Science, Class VIII. NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.77. Because gravity varies from place to place—for instance, gravity is much weaker on the Moon than on Earth—your weight will change depending on where you are, even though your mass remains constant.

Understanding how we measure these quantities is equally important. A spring balance is a common tool used to measure weight by calculating the pull of gravity on an object Science, Class VIII. NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.74. Interestingly, many digital weighing scales we use at home actually measure weight (force) but are calibrated to display the result in kilograms (mass) for convenience Science, Class VIII. NCERT (Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.142.

Feature	Mass	Weight
Definition	The amount of matter in an object.	The gravitational force acting on an object.
SI Unit	Kilogram (kg)	Newton (N)
Constancy	Remains the same everywhere.	Changes based on the local strength of gravity.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.74, 75, 77; Science, Class VIII. NCERT (Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.142

7. Solving the Original PYQ (exam-level)

Now that you have mastered the building blocks of mechanics, this question tests your ability to distinguish between the fundamental nature of physical laws. While you have learned that Newton’s Laws of Motion provide the general framework for how forces affect the state of an object, the Universal Law of Gravitation is a specific empirical discovery. The correct answer is (B) Newton's law of gravitation follows from Newton's laws of motion because it is the incorrect statement; these two sets of laws are independent. The Law of Gravitation was derived from observations of planetary motion and Kepler’s laws, rather than being a mathematical derivation or logical consequence of the three laws of motion.

To navigate this question like an expert, you must evaluate the scientific accuracy of each claim. Statement (A) is a core definition: the gravitational force is indeed universal and acts between all bodies. Statement (C) requires you to visualize the Earth's center, where the mass of the planet pulls you equally from every direction, leading to a net gravitational pull of zero. Finally, Statement (D) reinforces the distinction between mass (measured in kilograms) and weight (a force measured in newtons). UPSC often uses these fundamental distinctions to see if a student can separate conceptual definitions from mathematical relationships, as seen in Science, Class VIII, NCERT.