The mass of a body on Earth is 100 kg (acceleration due to gravity, ge - 10 m/s2). If acceleration due to gravity on the Moon ge/6, then the mass of the body on the moon is

1. Understanding Mass and Inertia (basic)

Welcome to the first step of your journey into mechanics! To understand how the universe moves, we must first understand the fundamental nature of "stuff" itself. In physics, we define Mass as the quantity of matter present in an object Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.141. Think of it as the total count of atoms and molecules packed into a body. Because this count doesn't change based on where you are, mass is an intrinsic property—it remains constant whether you are on the Earth, the Moon, or floating in deep space Science, Class VIII, Exploring Forces, p.75.

It is very common to confuse mass with Weight, but in science, they are distinct concepts. While mass is about matter, weight is the gravitational force exerted on that matter. On Earth, we often use these terms interchangeably because gravity is relatively uniform everywhere we go, but the distinction becomes clear when we change planets. For instance, the Moon’s surface gravity is much weaker than Earth's. If you take a 1 kg block to the Moon, its mass is still 1 kg, but it will feel much lighter because the force (weight) pulling it down has decreased Science, Class VIII, Exploring Forces, p.75.

Finally, mass is the direct measure of Inertia. Inertia is the inherent tendency of an object to resist any change in its state of rest or motion. The more mass an object has, the harder it is to start it moving, stop it, or change its direction. This is why it is much easier to push a pebble than a boulder—the boulder's greater mass gives it greater inertia, making it more "stubborn" against changes in motion.

To help you distinguish between the two, here is a quick comparison:

Sources: Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.75; Science, Class VIII. NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.141-142

2. Newton’s Second Law of Motion (F = ma) (basic)

Newton’s Second Law of Motion provides the mathematical backbone for understanding how objects move. It states that the Force (F) acting on an object is equal to the Mass (m) of that object multiplied by its Acceleration (a), expressed as the famous equation: F = ma. In simpler terms, if you want to speed up an object (acceleration), you need to apply a force, and the amount of force required depends directly on how much "stuff" or matter is in that object (its mass). A force can change an object’s speed, its direction, or both Science Class VIII, Exploring Forces, p. 77.

A critical distinction we must make here is between mass and weight. Mass is an intrinsic property of an object—it represents the quantity of matter it contains and remains constant no matter where the object is in the universe Science Class VIII, Exploring Forces, p. 75. Weight, however, is actually a force. Specifically, weight is the force of gravity acting upon a mass. While your mass would be the same on the Earth and the Moon, your weight would change because the Moon’s gravitational pull is much weaker Physical Geography by PMF IAS, Earths Interior, p. 58.

In the context of Newton's law, the SI unit of force is the newton (N) Science Class VIII, Exploring Forces, p. 77. One newton is defined as the amount of force needed to accelerate a 1 kg mass at a rate of 1 m/s². This law explains why it is much harder to push a heavy truck than a small bicycle; the larger mass requires a significantly greater force to achieve the same change in motion.

Sources: Science Class VIII, NCERT, Exploring Forces, p.75, 77; Physical Geography by PMF IAS, Earths Interior, p.58

3. The Universal Law of Gravitation (intermediate)

At its heart, the Universal Law of Gravitation states that every object in the universe exerts an attractive force on every other object. This force isn't just a local phenomenon on Earth; it is the "cosmic glue" that holds galaxies together and keeps planets in their orbits. According to this law, the gravitational force (F) between two bodies is directly proportional to the product of their masses (m₁ and m₂) and inversely proportional to the square of the distance (r) between their centers. This is expressed by the formula: F = G(m₁m₂ / r²), where G is the Universal Gravitational Constant Science, Class VIII, NCERT (Revised ed 2025), Chapter 5, p. 75.

One of the most critical distinctions you must master for the UPSC is the difference between mass and weight. Mass is an intrinsic property—it is the actual "amount of matter" in an object and does not change regardless of where you are in the universe. Weight, however, is a force. It is the measure of the gravitational pull exerted on that mass. For instance, while the Sun’s massive size exerts a gargantuan pull compared to Earth Physical Geography by PMF IAS, Chapter 2, p. 23, an astronaut's mass remains identical whether they are standing on the Sun (hypothetically!), the Moon, or Earth.

In modern physics, we've moved beyond Newton to understand gravity through Einstein's General Relativity. Here, gravity isn't just a "pulling force" but a curvature of spacetime itself. When massive objects like black holes or neutron stars collide, they create ripples in this fabric known as gravitational waves Physical Geography by PMF IAS, Chapter 1, p. 5. These waves are now used by scientists as "cosmic sirens" to measure the expansion rate of the universe, helping us refine our understanding of the Hubble constant Physical Geography by PMF IAS, Chapter 1, p. 6.

Sources: Science, Class VIII, NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.75; Physical Geography by PMF IAS, Chapter 2: The Solar System, p.23; Physical Geography by PMF IAS, Chapter 1: The Universe, p.5-6

4. Variation of 'g' (Acceleration due to Gravity) (intermediate)

When we talk about gravity, we must first distinguish between Mass and Weight. Mass is an intrinsic property of matter—it represents the actual quantity of matter in an object and remains constant regardless of where the object is located. Weight, however, is a force (W = m × g) that depends entirely on the local acceleration due to gravity (g). For instance, an object with a mass of 100 kg on Earth will still have a mass of 100 kg on the Moon, even though its weight would drop to about one-sixth because the Moon's surface gravity is much weaker Science, Class VIII NCERT (2025), Chapter 5, p. 75.

On Earth, the value of 'g' is not uniform everywhere. This variation is primarily due to the Earth's shape, which is an oblate spheroid (or Geoid). Because of the Earth's rotation, there is a centrifugal force that causes a bulge at the Equator and a flattening at the Poles. This means a person standing at the North Pole is actually closer to the Earth's center of mass than someone standing at the Equator. Since gravitational pull strengthens as distance decreases, the value of 'g' is greater at the poles and less at the equator Fundamentals of Physical Geography, NCERT Class XI (2025), Chapter 2, p. 19.

Furthermore, 'g' is influenced by the uneven distribution of mass within the Earth's crust. Variations in rock density or the presence of heavy mineral deposits can cause the measured gravity to differ from the expected theoretical value; this discrepancy is known as a gravity anomaly Physical Geography by PMF IAS, Chapter 2, p. 23. These anomalies are vital for geologists as they help map the internal structure of our planet. Additionally, as you move to higher altitudes (like the high mountain passes of the Himalayas), the distance from the Earth's center increases, causing the value of 'g' to decrease slightly.

Sources: Science, Class VIII NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.75; Fundamentals of Physical Geography, Geography Class XI (NCERT 2025 ed.), Chapter 2: The Origin and Evolution of the Earth, p.19; Physical Geography by PMF IAS (1st ed.), Chapter 2: The Solar System, p.23

5. Connected Concept: Weightlessness and Apparent Weight (exam-level)

To master mechanics, we must first distinguish between two terms often used interchangeably in daily life: mass and weight. Mass is an intrinsic property of an object, representing the actual "amount of matter" it contains Science, Class VIII, NCERT (Revised ed 2025), Chapter 5, p. 75. It is measured in kilograms (kg) and remains constant regardless of where the object is in the universe. Weight, however, is a force. It is the measure of the gravitational pull exerted on an object by a celestial body like Earth or the Moon. It is calculated using the formula W = m × g, where 'g' is the acceleration due to gravity. Because 'g' varies depending on your location (for instance, it is much weaker on the Moon), your weight changes even though your mass does not.

The concept of apparent weight is what we actually "feel" as our heaviness. When you stand on a scale, the scale doesn't technically measure the Earth's pull; it measures the normal force (the upward push) the scale exerts on your feet to keep you from falling. If you are in a stationary elevator, your apparent weight equals your true weight. However, if the elevator accelerates upward, the floor must push harder against you to move you up, making you feel heavier. Conversely, if the elevator accelerates downward, the floor pushes less, and you feel lighter. This sensation of changing heaviness despite constant mass is the core of apparent weight.

Weightlessness occurs when there is no supporting scale or floor pushing back against you. This happens during free fall. Imagine the cable of an elevator snaps; both you and the elevator would fall toward Earth at the same rate of acceleration ('g'). Because you are falling at the same speed as the floor, the floor exerts zero force on you. You would float inside the elevator, experiencing a state of weightlessness. It is important to realize that gravity is still acting on you—you haven't lost weight because gravity disappeared, but because you've lost the reaction force that allows you to feel that weight.

Sources: Science, Class VIII, NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.74-75

6. The Crucial Distinction: Mass vs. Weight (exam-level)

In physics, mass and weight are distinct concepts, though they are often used interchangeably in casual conversation. Mass represents the total quantity of matter present in an object Science, Class VIII, NCERT (Revised ed 2025), Chapter 9, p.142. It is an intrinsic property, meaning it does not change regardless of where the object is in the universe. Whether you are on Earth, the Moon, or floating in deep space, your mass remains identical because the "amount of stuff" making up the object hasn't changed. The standard units for mass are the gram (g) and kilogram (kg).

Weight, however, is a force—specifically, the gravitational force with which a planet or celestial body pulls an object toward itself Science, Class VIII, NCERT (Revised ed 2025), Chapter 5, p.75. Because weight is a force, its SI unit is the Newton (N). Crucially, weight depends on the local strength of gravity (g). Since gravitational force varies from planet to planet (and even slightly across different locations on Earth), an object's weight will change depending on its location, even while its mass remains constant Science, Class VIII, NCERT (Revised ed 2025), Chapter 5, p.77.

In our daily lives, we often say a bag of wheat "weighs 10 kg." Technically, 10 kg is the mass of the wheat. If you took that same bag to the Moon, its mass would still be 10 kg, but it would feel much lighter to lift because the Moon's gravitational pull is only about one-sixth that of Earth's Science, Class VIII, NCERT (Revised ed 2025), Chapter 5, p.75. Most digital scales we use actually measure weight (the force pressing down) but are calibrated to show the result in mass units (kg) for our convenience 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; Science, Class VIII, NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.77

7. Solving the Original PYQ (exam-level)

This question is a classic test of your fundamental understanding of the distinction between mass and weight, concepts we just explored in the learning path. While weight is a measure of the gravitational force acting on an object ($W = m \times g$), mass represents the actual quantity of matter within that object. As explained in Science, Class VIII. NCERT (Revised ed 2025), mass is an intrinsic property that remains constant regardless of the local gravitational field or location in the universe.

To arrive at the correct answer, a prepared aspirant must look past the numerical data provided for gravity ($g_e/6$). Since the question specifically asks for the mass of the body on the Moon, the answer is immediate: the quantity of matter does not change simply because the environment does. Therefore, a body with a mass of 100 kg on Earth will still have a mass of 100 kg on the Moon. As noted in Physical Geography by PMF IAS, while the Moon’s surface gravity is significantly weaker than Earth's, it only affects the weight (the downward force), not the fundamental mass.

The UPSC frequently uses options like 100/6 kg or 60 kg as distractors to catch students who reflexively perform calculations without pausing to identify the unit or property being requested. Option A is the most common trap, as it correctly identifies the gravitational ratio but incorrectly applies it to mass. By choosing 100 kg, you demonstrate that you can distinguish between scalar quantities (mass) and vector forces (weight), which is a vital skill for the Preliminary examination.