The weight of a body is 9.8 N at the place where g = 9.8 ms^2. Its mass is

1. Newton’s Laws of Motion and Force (basic)

Welcome to your journey into mechanics! To understand how the universe moves, we must first master the concept of Force. In its simplest form, a force is a push or a pull on an object resulting from its interaction with another object Science, Class VIII, Chapter 5, p.77. It is a vector quantity, meaning it has both magnitude and direction, and its standard SI unit is the newton (N) Science, Class VIII, Chapter 5, p.65. When you apply force, you can change an object’s speed, its direction of motion, or even its physical shape.

Forces are broadly categorized into two types: Contact forces, like the friction that slows down a rolling ball or the muscular force you use to lift a bag; and Non-contact forces, which act over a distance without physical touch. The most ubiquitous non-contact force is gravitational force. This is the attractive pull that the Earth exerts on all objects Science, Class VIII, Chapter 5, p.72. Unlike magnetic or electrostatic forces, which can both pull (attract) and push (repel), gravity is always attractive.

One of the most important distinctions you must make for the UPSC exam is between mass and weight. Mass (m) is the actual quantity of matter in an object and remains constant regardless of where you are in the universe; it is measured in kilograms (kg). Weight (W), however, is the force of gravity acting on that mass. We calculate it using the formula: W = m × g, where 'g' is the acceleration due to gravity (approximately 9.8 m/s² on Earth). Because weight is a force, its unit is the Newton, not the kilogram Science, Class VIII, Chapter 5, p.72.

Sources: Science, Class VIII . NCERT(Revised ed 2025), Chapter 5: Exploring Forces, p.65, 69, 72, 77

2. Understanding SI Units and Measurements (basic)

In the world of science, we need a universal language to ensure that a 'meter' in New Delhi is exactly the same as a 'meter' in New York. This language is the International System of Units (SI). At its foundation, we have fundamental units like the kilogram (kg) for mass, the meter (m) for length, and the second (s) for time. When we combine these fundamental units, we create derived units. For instance, since speed is distance divided by time, its SI unit is the meter per second (m/s) Science - Class VII, Measurement of Time and Motion, p.113. Similarly, density—which tells us how much matter is packed into a space—is calculated as mass divided by volume, giving us the SI unit kilogram per cubic meter (kg/m³) Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.141.

One of the most critical distinctions you must master for the UPSC is the difference between mass and weight. In everyday life, we often use them interchangeably, but in physics, they are distinct concepts. Mass is the actual quantity of matter in an object and remains constant regardless of where you are in the universe. Weight, however, is the force of gravity pulling on that mass Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.142. This relationship is expressed by the formula W = m × g, where 'g' is the acceleration due to gravity. Because weight is a force, its SI unit is the Newton (N), while mass is measured in kilograms (kg).

Finally, consider pressure, which is defined as the force applied per unit area. Since force is measured in Newtons and area in square meters, the SI unit is N/m², which is also known as the Pascal (Pa) Science, Class VIII, Pressure, Winds, Storms, and Cyclones, p.82. Understanding these units allows us to quantify the physical world with precision, moving from simple observations to exact scientific measurements.

Sources: Science - Class VII, Measurement of Time and Motion, p.113; Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.141; Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.142; Science, Class VIII, Pressure, Winds, Storms, and Cyclones, p.82

3. Universal Law of Gravitation (intermediate)

At its heart, the Universal Law of Gravitation explains why the universe doesn't simply drift apart. Formulated by Isaac Newton, this theory was the climax of the scientific revolution, providing a mathematical framework for the force that keeps our feet on the ground and planets in their orbits Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119. Unlike magnetism, which can pull or push, 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. NCERT (2025 ed.), Chapter 5: Exploring Forces, p.72.

To master this concept, you must distinguish between two terms often used interchangeably in daily life: Mass and Weight. Mass is the actual quantity of matter in an object and remains constant regardless of where you are in the universe. Weight, however, is a measure of the gravitational pull exerted on that mass. We calculate weight using the formula W = m × g, where 'W' is weight in Newtons (N), 'm' is mass in kilograms (kg), and 'g' is the acceleration due to gravity (approximately 9.8 m/s² on Earth). This means a 1 kg mass on Earth weighs approximately 9.8 N.

Interestingly, gravity is not perfectly uniform across the Earth's surface. Because the Earth's mass is not distributed evenly within its crust, the strength of gravity fluctuates slightly from one location to another. Geologists call these variations gravity anomalies, and they use them to map the materials hidden deep beneath the Earth's surface Physical Geography by PMF IAS, Earths Interior, p.58. On a much larger cosmic scale, when mass becomes incredibly dense—such as in a dying star—the gravitational pull can become so intense that it creates a singularity, where even light cannot escape, leading to the formation of a black hole Physical Geography by PMF IAS, The Universe, p.7.

Sources: Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119; Science, Class VIII. NCERT (2025 ed.), Chapter 5: Exploring Forces, 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

4. Variation of 'g' and its Effects (intermediate)

In our journey through mechanics, understanding the difference between mass and weight is fundamental. While we often use these terms interchangeably in daily life, physics draws a sharp line between them. Mass (m) is the actual quantity of matter contained in a body and remains constant regardless of where you are in the universe. Weight (W), however, is the force with which the Earth attracts that mass. It is calculated using the formula W = m × g, where 'g' is the acceleration due to gravity. Because 'g' is not a universal constant but varies based on your location, your weight changes even if your mass stays the same Science, Class VIII NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p. 72.

The Earth is not a perfect sphere; it is an oblate spheroid or Geoid—slightly flattened at the poles and bulging at the equator due to its rotation. This shape significantly impacts the value of 'g'. Because the equatorial radius is larger than the polar radius, a person at the equator is further from the Earth's center of mass than a person at the poles. Consequently, gravity is strongest at the poles and weakest at the equator Physical Geography by PMF IAS, Latitudes and Longitudes, p. 241. Additionally, the Earth's rotation creates a centrifugal force that is maximum at the equator, further counteracting the pull of gravity and reducing the effective value of 'g' in that region.

Beyond latitude, 'g' also varies due to the uneven distribution of mass within the Earth's crust. Geologists measure these deviations from expected gravity values, referring to them as gravity anomalies. These anomalies provide crucial data about the density of materials beneath the surface, such as mineral deposits or tectonic structures FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p. 19. Furthermore, as you move to higher altitudes, the distance from the Earth's center increases, causing 'g' (and thus your weight) to decrease further.

Sources: Science, Class VIII NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.72; Physical Geography by PMF IAS, Latitudes and Longitudes, p.241; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19

5. Scalar and Vector Quantities in Mechanics (intermediate)

In mechanics, we categorize physical quantities into two fundamental types based on whether they require a direction to be fully understood: Scalars and Vectors. A Scalar quantity is described solely by its magnitude (size or numerical value). Common examples include time, temperature, distance, and mass. As defined in scientific principles, mass represents the "quantity of matter present in any object" Science, Class VIII (NCERT), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.141. Because mass does not change based on which way an object is facing or moving, it is a pure scalar.

Conversely, a Vector quantity requires both magnitude and direction to be complete. If you tell someone to "apply a force of 10 Newtons," their first question will be "In which direction?" This is because force is a vector. A critical vector in mechanics is weight, which is the force of Earth's gravitational attraction acting on an object Science, Class VIII (NCERT), Chapter 5: Exploring Forces, p.72. Unlike mass, weight always acts in a specific direction—downward toward the center of the Earth.

The relationship between these two is expressed by the formula W = m × g, where weight (W) is a vector, mass (m) is a scalar, and g is the acceleration due to gravity (a vector). This distinction explains why your mass remains 1 kg everywhere in the universe, but your weight would change if you moved from Earth to the Moon, as the gravitational pull (the vector field) changes Science, Class VIII (NCERT), Chapter 5: Exploring Forces, p.75. In everyday language, we often use "weight" when we mean "mass" (e.g., saying a bag weighs 10 kg), but in physics, we must be precise: mass is in kilograms (scalar), and weight is in Newtons (vector).

Sources: Science, Class VIII (NCERT), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.141; Science, Class VIII (NCERT), Chapter 5: Exploring Forces, p.72, 75

6. Core Concept: Mass vs. Weight (exam-level)

In common conversation, we often use the terms "mass" and "weight" interchangeably, but in the realm of physics and competitive exams, 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 body, meaning it remains constant regardless of where the object is located in the universe. Whether you are on the peak of Mt. Everest, at the bottom of the Mariana Trench, or floating in the vacuum of space, your mass does not change. Its standard units are the gram (g) and kilogram (kg).

Weight, on the other hand, is not an inherent property of the object itself, but a measure of the gravitational force with which a planet (like Earth) attracts that object Science, Class VIII. NCERT (Revised ed 2025), Chapter 5, p.75. Because weight is a force, it is measured in Newtons (N). The relationship between the two is governed by the formula: W = m × g, where 'W' is weight, 'm' is mass, and 'g' is the acceleration due to gravity. On Earth, the standard value of g is approximately 9.8 m/s². This means an object with a mass of 1 kg will exert a weight of 9.8 N (1 kg × 9.8 m/s² = 9.8 N).

Because weight depends on gravity, it is variable. Gravity can change slightly due to Earth's shape and density—for instance, gravity measurements in deep oceanic trenches have shown anomalies where the value of g is lower due to a loss of material mass in those zones Physical Geography by PMF IAS, Tectonics, p.108. If you were to travel to the Moon, where gravity is much weaker, your weight would decrease significantly, even though your mass remains exactly the same. Most weighing scales we use are actually measuring this downward force (weight) but are calibrated to show the reading in mass units (kg) for practical everyday use Science, Class VIII. NCERT (Revised ed 2025), Chapter 9, p.142.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.142; Science, Class VIII. NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.75; Physical Geography by PMF IAS, Tectonics, p.108

7. Numerical Application of the Weight Formula (exam-level)

In physics, understanding the distinction between mass and weight is fundamental to solving mechanics problems. While we often use these terms interchangeably in daily life (like when calculating Body Mass Index or BMI in kilograms), they represent two very different physical concepts. Mass (m) is the actual quantity of matter contained in an object and is measured in kilograms (kg); it remains constant regardless of where you are in the universe. In contrast, Weight (W) is the gravitational force exerted by a celestial body (like Earth) on that mass, and it is measured in Newtons (N). This relationship is mathematically expressed by the formula: W = m × g, where 'g' represents the acceleration due to gravity.

When you are asked to find the mass of an object based on its weight, you must rearrange this formula to isolate mass: m = W / g. For instance, if a spring balance measures an object's weight as 9.8 N at a location where the acceleration due to gravity is 9.8 m/s², the calculation becomes simple: m = 9.8 N / 9.8 m/s², which equals exactly 1 kg. This numerical application highlights that while the weight is a force of attraction, the mass is a property of the object itself. You can find more details on how these measurements are conducted using instruments like spring balances in Science, Class VIII. NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p. 74.

It is important to note that for most practical purposes on Earth, because gravity is relatively uniform, we can use the weight of an object to reliably determine its mass. However, in scientific contexts and competitive exams, keeping the units distinct—Newtons for force/weight and kilograms for mass—is crucial for accuracy. As noted in Science, Class VIII. NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p. 75, mass stays the same at every place, whereas weight reflects the pull of the Earth at that specific point.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.72, 74-75; Understanding Economic Development. Class X. NCERT (Revised ed 2025), DEVELOPMENT, p.12

8. Solving the Original PYQ (exam-level)

This question brings together your understanding of force, gravitational acceleration, and the crucial distinction between mass and weight. As you've learned, mass is an intrinsic property representing the amount of matter in an object, while weight is the gravitational force acting upon it. The bridge between these two concepts is the fundamental formula W = m × g, as detailed in Science, Class VIII NCERT (Revised ed 2025). Here, the UPSC is testing your ability to apply this relationship mathematically while keeping your units straight.

To solve this, we simply rearrange our building blocks: if weight (W) is the product of mass (m) and acceleration due to gravity (g), then mass equals weight divided by gravity (m = W/g). By substituting the given values—a weight of 9.8 N and a 'g' of 9.8 m/s²—the calculation becomes 9.8 / 9.8, which yields exactly 1 kg. It is vital to remember that while the numerical value of weight can change depending on the local gravity, the mass remains constant regardless of location, a principle emphasized by the NASA Glenn Research Center.

UPSC often includes "distractor" options to catch students who rush. Option (B) 9.8 kg is a classic trap designed to trick those who fail to distinguish between the magnitude of force and the unit of mass. Option (A) zero is physically impossible for a "body," and Option (C) 10 kg is a common error for those used to rounding 'g' to 10 m/s² without looking at the specific values provided in the prompt. Always verify the units and the specific constants given to arrive at the correct answer (D).