The weight of an object may be assigned using Newton’s

1. Newton’s First Law and the Concept of Inertia (basic)

Newton’s First Law of Motion, often called the Law of Inertia, serves as the foundation of classical mechanics. At its simplest, it tells us that objects are "stubborn." If an object is at rest, it wants to stay at rest. If it is moving in a straight line at a constant speed—what we call uniform linear motion—it wants to keep moving that way forever Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.118. This state of affairs only changes when an external force (a push or a pull) acts upon the object to break its equilibrium Science ,Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.77.

The term Inertia refers to this inherent property of matter to resist any change in its state of motion. It is important to understand that inertia is not a force itself, but a quality of an object. The amount of inertia an object possesses is directly proportional to its mass. For example, it is much harder to push a stationary car into motion than a stationary bicycle because the car has more mass and, therefore, greater inertia. This concept is so fundamental that we even see it applied metaphorically in other fields, such as "industrial inertia," where established industries resist moving to new locations despite changing economic advantages Environment and Ecology, Majid Hussain, Locational Factors of Economic Activities, p.32.

To visualize this law, consider the forces at play. A force can change an object’s speed, its direction, or both Science ,Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.77. Without such a force—like friction or gravity—an object in space would glide in a straight line at the same speed indefinitely. In our daily lives, we don't always see this because invisible forces like friction eventually slow things down, but the principle remains: motion does not require a force to maintain it; force is only required to change it.

Condition	Behavior due to Inertia	Required to change
Object at Rest	Stays stationary	Unbalanced External Force
Object in Motion	Stays in uniform linear motion	Unbalanced External Force

Sources: Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.118; Science ,Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.77; Environment and Ecology, Majid Hussain, Locational Factors of Economic Activities, p.32

2. Momentum and the Quantitative Definition of Force (intermediate)

To understand how we measure force, we must first understand momentum. Momentum is often described as the 'quantity of motion' an object possesses. It is the product of an object's mass (m) and its velocity (v), represented by the formula p = mv. Because velocity has a direction, momentum is also a vector quantity. This concept is crucial because it explains why a heavy truck moving slowly can have as much 'impact' as a light bullet moving very fast — they both possess high momentum.

Newton’s Second Law of Motion provides the quantitative definition of force. It states that the magnitude of a force is equal to the rate of change of momentum over time. When the mass of an object remains constant, this relationship simplifies into the famous equation F = ma (Force = mass × acceleration). This tells us that to change the motion of an object (accelerate it), we must apply a force proportional to both its mass and the desired change in velocity. The SI unit for force is the Newton (N), which is defined as the force required to accelerate 1 kg of mass at 1 m/s² Science, Class VIII . NCERT (Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p. 94.

A practical and universal application of this law is the calculation of Weight. While we often use 'mass' and 'weight' interchangeably in daily life, they are scientifically distinct. Mass is the amount of matter in an object, whereas weight is the gravitational force with which the Earth attracts that object. By applying Newton's second law (F = ma), we can define weight (W) as the product of mass (m) and the acceleration due to gravity (g). Thus, the formula is W = mg Science, Class VIII . NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p. 72. This is why your weight would change on the Moon (where gravity is weaker), even though your mass remains exactly the same Science, Class VIII . NCERT (Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p. 142.

Sources: Science, Class VIII . NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.72; Science, Class VIII . NCERT (Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.94; Science, Class VIII . NCERT (Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.142

3. Newton’s Third Law and Interaction of Forces (basic)

In our previous discussions, we looked at how force can change motion. But where does force actually come from? Newton’s Third Law tells us that force is never a solo act; it is always an interaction between two objects. A force is a push or pull on an object resulting from its interaction with another object Science, Class VIII . NCERT(Revised ed 2025), Exploring Forces, p. 77. This means that forces always exist in pairs. If you push against a wall, the wall pushes back on you with the exact same amount of force. Formally, Newton’s Third Law states: "To every action, there is always an equal and opposite reaction." It is vital to understand that 'action' and 'reaction' are just names for the two forces in an interaction. They are equal in magnitude (strength) and opposite in direction. Most importantly, they act on different objects. For example, when you walk, your foot pushes the ground backward (action), and the ground pushes your foot forward (reaction). Because these forces act on different bodies—one on the ground and one on you—they do not cancel each other out, allowing you to move forward. This principle applies to all types of forces, whether they are contact forces like friction or non-contact forces like gravity Science, Class VIII . NCERT(Revised ed 2025), Exploring Forces, p. 77. For instance, the Earth pulls on the Moon with a gravitational force, and the Moon pulls back on the Earth with an identical force. Whether it is a magnet attracting an iron nail or a person sitting on a chair, the interaction is always mutual and simultaneous.

Sources: Science, Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.77

4. The Universal Law of Gravitation (intermediate)

At its heart, the Universal Law of Gravitation tells us that every object in the universe with mass exerts an attractive pull on every other object. Unlike magnetism or static electricity, which can both push and pull, gravity is strictly an attractive force. It is also a non-contact force, meaning it acts across a distance without needing physical touch Science, Class VIII, Exploring Forces, p. 72. While we often think of gravity as a "downward" pull toward the center of the Earth, it is actually a property of mass itself; the more massive an object, the stronger its gravitational influence.

To understand how we quantify this pull, we look at the concept of Weight. While mass is the amount of matter in an object, weight is the gravitational force with which a large body (like Earth) attracts that mass. This is a direct application of Newton’s Second Law of Motion (F = ma). In the context of gravity, the force (F) becomes Weight (W), and the acceleration (a) becomes the acceleration due to gravity (g). Thus, we arrive at the fundamental formula: W = mg Science, Class VIII, Weight and Its Measurement, p. 72. Because weight is a force, it is measured in Newtons (N), not kilograms.

Interestingly, gravity is not uniform everywhere on Earth. Because the Earth’s crust has an uneven distribution of material and mass, the gravitational pull varies slightly from one location to another. Geologists call these differences gravity anomalies, and they use them to map the Earth’s interior Physical Geography by PMF IAS, Earths Interior, p. 58. On an even grander scale, when mass becomes incredibly concentrated—such as in stars exceeding the Chandrasekhar Limit—gravity becomes so intense that it can lead to the formation of a singularity, where our standard laws of physics begin to break down Physical Geography by PMF IAS, The Universe, p. 7.

Feature	Mass	Weight
Definition	The quantity of matter in an object.	The force of gravity acting on an object.
Formula	Scalar (m)	Vector (W = mg)
Variability	Constant everywhere in the universe.	Changes based on the local gravitational field.

Sources: Science, Class VIII (NCERT 2025), Exploring Forces, p.72; Science, Class VIII (NCERT 2025), Weight and Its Measurement, p.72; 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

5. Distinction Between Mass and Weight (intermediate)

In common conversation, we often use the terms mass and weight as if they mean the same thing. However, in the realm of physics—and for your UPSC preparation—distinguishing between them is vital. Mass is defined as the actual quantity of matter present in an object Science, Class VIII . NCERT(Revised ed 2025), Chapter 9, p.142. It is an intrinsic property of the object; whether you are on the Earth, the Moon, or floating in deep space, 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 inherent property but a force. Specifically, it is the gravitational force with which a planet (like Earth) pulls an object toward itself Science, Class VIII . NCERT(Revised ed 2025), Chapter 5, p.75. This relationship is a direct application of Newton’s Second Law of Motion (F = ma). When we talk about weight, the force (F) is Weight (W), and the acceleration (a) is the acceleration due to gravity (g). Therefore, the mathematical formula is W = mg. Because weight depends on gravity, it can change depending on your location. For instance, the weight of an object on the Moon is only about one-sixth of its weight on Earth because the Moon's gravitational pull is much weaker Science, Class VIII . NCERT(Revised ed 2025), Chapter 5, p.78.

To keep these concepts clear, it helps to look at how we measure them. We measure mass in kilograms (kg) or grams (g), while weight, being a force, is measured in newtons (N). A common tool for measuring weight is the spring balance, which stretches based on the force applied to it Science, Class VIII . NCERT(Revised ed 2025), Chapter 5, p.74. Interestingly, most digital weighing scales we use daily actually measure the force (weight) you exert, but their displays are calibrated to show the value in mass units (kg) for our convenience Science, Class VIII . NCERT(Revised ed 2025), Chapter 9, p.142.

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Gravitational pull acting on an object.
Type of Quantity	Scalar (Magnitude only).	Vector (Directed towards the center of the planet).
Variability	Constant everywhere.	Changes with gravity (location).
SI Unit	Kilogram (kg).	Newton (N).

Sources: Science, Class VIII . NCERT(Revised ed 2025), Chapter 5: Exploring Forces, p.74, 75, 78; Science, Class VIII . NCERT(Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.142

6. Defining Weight as a Derivative of the Second Law (exam-level)

To understand weight, we must first look at its parent principle: Newton’s Second Law of Motion. This law states that the net force (F) acting on an object is equal to the product of its mass (m) and its acceleration (a), expressed as F = ma. In the context of our planet, the Earth exerts a constant gravitational pull on everything near its surface. This specific gravitational force is what we call weight.

Weight is essentially a specific application of the Second Law. Instead of a general force (F), we use Weight (W); and instead of a general acceleration (a), we use the acceleration due to gravity (g). Thus, the formula transforms into W = mg. Because weight is fundamentally a force, it is measured in Newtons (N), just like any other force in physics Science, Class VIII NCERT (2025), Exploring Forces, p. 72. This is why, scientifically speaking, it is incorrect to say a bag of wheat "weighs 10 kg"—10 kg is its mass, while its weight is the force resulting from that mass being pulled by gravity.

A crucial takeaway from the relationship W = mg is that while an object’s mass remains constant regardless of its location, its weight is variable. Since the acceleration due to gravity (g) differs depending on where you are in the universe—or even where you are on Earth—your weight will change accordingly Science, Class VIII NCERT (2025), Exploring Forces, p. 77. For instance, the gravitational pull on the Moon is much weaker than on Earth, leading to a significant reduction in weight despite the mass remaining the same.

Feature	Mass (m)	Weight (W)
Definition	The amount of matter in an object.	The force of gravity acting on an object.
Formula	Intrinsic property (m)	Derived from 2nd Law (W = mg)
SI Unit	Kilogram (kg)	Newton (N)
Variability	Constant everywhere.	Changes with gravity (location).

Sources: Science, Class VIII NCERT (2025), Exploring Forces, p.72; Science, Class VIII NCERT (2025), Exploring Forces, p.77

7. Solving the Original PYQ (exam-level)

Now that you have mastered the concepts of mass, acceleration, and force, this question brings them all together into a single application: weight. In physics, weight is not just a measurement on a scale; it is the specific gravitational force exerted by the Earth on an object. To solve this, you must recall the bridge between force and motion you just studied—Newton’s second law of motion. While the first law defines inertia and the third explains interactions, the second law provides the actual mathematical framework ($F = ma$) needed to calculate or "assign" a value to any force.

To arrive at the correct answer, think like a physicist: if weight ($W$) is a force, it must follow the rule $F = ma$. When an object is under the influence of gravity, the acceleration ($a$) becomes the acceleration due to gravity ($g$). Therefore, the formula $W = mg$ is a direct application of the second law, as noted in Science, Class VIII, NCERT (Revised ed 2025). This makes (B) second law of motion the correct choice because it is the only law that provides a functional equation to determine the magnitude of force based on mass.

UPSC often includes distractors like "laws of gravitation" (Option D) to test your precision. While the law of gravitation explains why two masses attract, it is the second law that tells us how much force is produced in terms of motion variables. Options (A) and (C) are incorrect because the first law describes the tendency to resist change (inertia) and the third law describes the nature of interaction pairs, neither of which is used to mathematically assign the weight of a single object.