A body weighs 5 kg on equator. At the poles, it is likely to weigh

1. Distinguishing Mass vs. Weight (basic)

To master basic mechanics, we must first clear a very common confusion: the difference between mass and weight. While we often use these terms interchangeably in grocery stores or at the gym, they represent two fundamentally different concepts in physics. Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.142

Mass is the measure of the actual quantity of matter contained within an object. It is an intrinsic property, meaning it does not change regardless of where the object is located in the universe. If you have a 5 kg block of iron, it remains 5 kg whether it is on Earth, the Moon, or floating in deep space. Mass is measured in kilograms (kg) or grams (g).

Weight, on the other hand, is a force. Specifically, it is the gravitational force exerted by a celestial body (like Earth) on an object. Because weight is a force, its SI unit is the newton (N). Science, Class VIII, Exploring Forces, p.77. Weight is calculated using the formula W = mg, where 'm' is mass and 'g' is the acceleration due to gravity.

Crucially, weight varies from place to place because gravity is not uniform everywhere. For example, because the Moon's gravity is much weaker than Earth's, your weight on the Moon would be about one-sixth of your weight on Earth, even though your mass remains identical. Science, Class VIII, Exploring Forces, p.75. Even on Earth, your weight changes slightly based on your location. The Earth is an oblate spheroid (bulging at the equator and flattened at the poles). Since the poles are closer to the Earth’s center than the equator is, the gravitational pull is stronger at the poles. Additionally, Earth's rotation creates a centrifugal force that acts outward at the equator, slightly reducing the effective gravity there. Therefore, an object will weigh slightly more at the North Pole than it does at the Equator.

Feature	Mass	Weight
Definition	Amount of matter in an object.	Gravitational force acting on an object.
Constancy	Constant everywhere.	Varies depending on local gravity.
SI Unit	Kilogram (kg).	Newton (N).
Measurement tool	Two-pan balance (physical balance).	Spring balance or digital scale.

Sources: Science, Class VIII (Revised 2025), The Amazing World of Solutes, Solvents, and Solutions, p.142; Science, Class VIII (Revised 2025), Exploring Forces, p.74-77

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

At the heart of classical mechanics lies Newton’s Law of Universal Gravitation, a concept that revolutionized our understanding of the cosmos by proving that the same force pulling an apple to the ground also keeps the planets in orbit Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119. The law states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, this is expressed as F = G(m₁m₂/r²), where G is the universal gravitational constant. This means if you double the mass of one object, the pull doubles; but if you double the distance between them, the pull drops to one-fourth.

While we often treat gravity as a constant on Earth (approx. 9.8 m/s²), it actually fluctuates depending on where you stand. This is primarily because the Earth is not a perfect sphere; it is an oblate spheroid, meaning it bulges at the equator and is flattened at the poles. Because the poles are physically closer to the Earth's center (a smaller 'r' in our formula), the gravitational pull is significantly stronger there than at the equator Fundamentals of Physical Geography, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19. Additionally, the Earth's rotation creates a centrifugal force that acts outward, effectively 'canceling' a tiny fraction of gravity at the equator, further making you feel lighter there than at the poles.

Beyond just geography, the actual composition of the Earth beneath your feet matters. The distribution of mass within the crust is uneven—some areas have dense ores, while others have lighter materials. This causes the observed gravity to differ from the theoretically expected value, a phenomenon known as a gravity anomaly Physical Geography by PMF IAS, Earths Interior, p.58. These anomalies are vital for geologists because they act like a 'X-ray' for the Earth's crust, helping us map out hidden mineral deposits and understand the structural variations of our planet.

Feature	Equator	Poles
Distance from Center (r)	Greater (Bulge)	Smaller (Flattened)
Gravitational Pull (g)	Lower (~9.78 m/s²)	Higher (~9.83 m/s²)
Centrifugal Force	Maximum (Outward push)	Zero
Your Weight	Lower	Higher

Sources: Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119; 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. Understanding Acceleration due to Gravity (g) (intermediate)

In our previous steps, we looked at motion and forces; now, we dive into the specific force that governs almost every physical process on our planet: gravity. While we often treat the acceleration due to gravity (g) as a constant 9.8 m/s², it is actually a variable that changes depending on where you are standing. In physical geography, gravity is the "master switch"—without it, there would be no gradients, no downward movement of water, and no geomorphic processes like erosion or deposition Fundamentals of Physical Geography, Geography Class XI (NCERT 2025 ed.), Geomorphic Processes, p.38.

The variation in g is primarily driven by two factors: the Earth's shape and its rotation. First, the Earth is an oblate spheroid, meaning it is slightly flattened at the poles and bulges at the equator. Because the gravitational pull is inversely proportional to the square of the distance from the center, the poles (which are closer to the center) experience a stronger pull than the equator. Second, as the Earth rotates, it generates a centrifugal force that acts outward. This force is strongest at the equator and zero at the poles, effectively "canceling out" a tiny portion of gravity at the equator.

Feature	At the Equator	At the Poles
Distance from Center	Greater (Equatorial Bulge)	Shorter (Flattened)
Centrifugal Force	Maximum (acts outward)	Zero
Value of 'g'	Lower (~9.78 m/s²)	Higher (~9.83 m/s²)

Furthermore, gravity isn't even uniform across the same latitude. The uneven distribution of mass within the Earth's crust—such as dense ore deposits or mountain ranges—causes local variations known as gravity anomalies Fundamentals of Physical Geography, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19. These anomalies are vital for geologists to understand the materials hidden beneath the surface. It is also fascinating to note that while Earth's g is 9.8 m/s², the Sun’s surface gravity is a staggering 274 m/s², whereas the Moon’s is a mere 1.62 m/s² Physical Geography by PMF IAS, The Solar System, p.23.

Sources: Fundamentals of Physical Geography, Geography Class XI (NCERT 2025 ed.), Geomorphic Processes, p.38; Fundamentals of Physical Geography, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19; Physical Geography by PMF IAS, The Solar System, p.23

4. Earth's Shape: The Oblate Spheroid (intermediate)

Concept: Earth's Shape: The Oblate Spheroid

5. Centrifugal Force and Earth's Rotation (intermediate)

To understand how the Earth's rotation affects us, we must first look at the centrifugal force. Imagine standing on a fast-spinning merry-go-round; you feel a push directed outward, away from the center. Similarly, as the Earth rotates on its axis from west to east once every 24 hours Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.251, it generates a centrifugal force that acts outward, away from the Earth's axis of rotation. This force acts as a 'counter-force' to gravity. While gravity pulls everything toward the center of the Earth, the centrifugal force tries to fling objects into space.

The intensity of this centrifugal force is not uniform across the globe; it depends entirely on the speed of rotation at a specific latitude. Because the Earth's circumference is greatest at the equator, a point on the equator must travel much faster to complete a rotation in 24 hours compared to a point near the poles. In fact, the speed of rotation is at its maximum at the equator and effectively zero at the poles Physical Geography by PMF IAS, Latitudes and Longitudes, p.241. Consequently, the centrifugal force is strongest at the equator and vanishes at the North and South Poles.

This variation has a direct impact on your effective weight. Weight is the net gravitational pull you feel. At the equator, the strong outward centrifugal force cancels out a small portion of the inward gravitational pull. Furthermore, because the Earth is an oblate spheroid (it bulges at the middle), the equator is further from the Earth's center than the poles are Physical Geography by PMF IAS, Tectonics, p.95. These two factors—the greater distance from the center and the maximum centrifugal force—result in a lower gravitational acceleration (g) at the equator (~9.76 m/s²) compared to the poles (~9.86 m/s²). Therefore, an object will always weigh slightly less at the equator than it does at the poles.

Feature	At the Equator	At the Poles
Rotational Speed	Maximum (~1,670 km/hr)	Zero
Centrifugal Force	Maximum (acts outward)	Zero
Distance to Earth's Center	Greater (Equatorial Bulge)	Shorter
Effective Weight	Minimum	Maximum

Sources: Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.251; Physical Geography by PMF IAS, Latitudes and Longitudes, p.241; Physical Geography by PMF IAS, Tectonics, p.95

6. Adjacent Concept: Orbital Motion and Escape Velocity (exam-level)

To understand how satellites stay in space or how we send missions to Mars, we must grasp the distinction between Orbital Velocity and Escape Velocity. Imagine throwing a ball horizontally: the harder you throw, the further it goes before hitting the ground. If you throw it at a specific, high speed (approx. 7.9 km/s for Earth), the rate at which the ball 'falls' matches the curvature of the Earth. It never hits the ground; instead, it enters a state of continuous fall known as an orbit. This speed is not fixed if the path is elliptical; as explained in Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.257, a planet or satellite moves fastest at its perigee (closest point) and slowest at its apogee (farthest point), a phenomenon governed by Kepler’s Second Law.

While orbital velocity keeps an object trapped in a gravitational loop, Escape Velocity is the 'exit ticket' required to break free from a planet's pull entirely. It is the minimum speed a non-propelled object needs to reach to travel to 'infinity' without being pulled back. For Earth, this is roughly 11.2 km/s. A key point for your exams: escape velocity depends only on the mass and radius of the celestial body (like Earth or the Moon), not on the mass of the object trying to escape. This is why a tiny spark and a massive rocket both need the same velocity to leave Earth.

The relationship between these two is precise: for any planet, the escape velocity is exactly √2 (approx. 1.41) times the velocity required for a circular orbit near the surface. In the realm of geography and space science, this explains why the Earth retains its atmosphere (gas molecules don't reach escape velocity) while the Moon, with its much lower escape velocity, cannot. As we see in planetary dynamics, Earth's distance from the Sun also affects its speed; in the Northern Hemisphere summer, the Earth is farther from the Sun, moving at its lowest orbital velocity, which actually makes our summers slightly longer than our winters Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.256.

Sources: Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.257; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.256

7. Variation of 'g' with Latitude (exam-level)

Hello! Today we are exploring a fascinating nuance of our planet: why your weight actually changes slightly depending on your latitude. While we often use a standard value for the acceleration due to gravity (g ≈ 9.8 m/s²), in reality, 'g' is not uniform across the Earth's surface. This variation is driven by two primary physical factors: the Earth's shape and its rotation.

First, let’s look at the Earth's shape. Our planet is not a perfect sphere; it is an oblate spheroid (often called a Geoid). Due to billions of years of rotation, the Earth has developed a "bulge" at the Equator and a slight flattening at the North and South Poles Physical Geography by PMF IAS, Latitudes and Longitudes, p.241. This means that if you are standing at a pole, you are physically closer to the Earth's center of mass than if you were standing at the Equator. Since gravitational pull strengthens as distance decreases, the Earth's mass pulls more strongly on objects at the poles.

Second, we must account for the centrifugal force caused by the Earth's rotation. As the Earth spins on its axis, every object on its surface experiences an outward force, much like being pushed to the side on a spinning merry-go-round. This centrifugal force is at its maximum at the Equator, where the rotational speed is highest, and it reduces to zero at the poles, which sit directly on the axis of rotation Physical Geography by PMF IAS, Latitudes and Longitudes, p.241. Because this force acts outward (away from the center), it effectively opposes and weakens the inward pull of gravity at lower latitudes.

As you travel from the Equator toward either pole, your latitude increases from 0° toward 90° Exploring Society: India and Beyond, NCERT Class VI, Locating Places on the Earth, p.14. During this journey, the effective value of 'g' gradually increases because you are getting closer to the center of the Earth and the opposing centrifugal force is vanishing.

Feature	Equator (0° Latitude)	Poles (90° Latitude)
Distance from Center	Greater (Equatorial Bulge)	Lesser (Flattened)
Centrifugal Force	Maximum (outward push)	Zero
Value of 'g'	Minimum (~9.78 m/s²)	Maximum (~9.83 m/s²)

Sources: Physical Geography by PMF IAS, Latitudes and Longitudes, p.241; Exploring Society: India and Beyond. Social Science-Class VI . NCERT, Locating Places on the Earth, p.14

8. Solving the Original PYQ (exam-level)

Now that you have mastered the concepts of Earth's geometry and gravitational dynamics, this question serves as the perfect test of how those building blocks interact. To arrive at the correct conclusion, you must synthesize two key principles: the oblate spheroid shape of the Earth and the effect of centrifugal force. As you learned from FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), the Earth is not a perfect sphere; it bulges at the equator and is flattened at the poles. This means a person at the poles is physically closer to the Earth's center of mass than someone at the equator. Because the gravitational pull strengthens as distance decreases, the acceleration due to gravity is naturally higher at the poles.

As your coach, I want you to walk through the logic step-by-step: Weight is mass multiplied by gravity (W = m x g). While mass remains constant everywhere, the 'g' factor changes. At the equator, the Earth's rotation is at its fastest, creating a centrifugal force that acts outward, effectively "lifting" the object slightly and reducing its measured weight. At the poles, this rotation speed—and the resulting centrifugal force—drops to zero. Combined with the shorter polar radius, the effective gravity increases from approximately 9.78 m/s² at the equator to 9.83 m/s² at the poles. Consequently, the body must weigh (D) more than 5 kg when moved to the poles.

UPSC designed the other options to test common conceptual slips. Option (A) is a classic trap for students who confuse mass (which stays 5 kg) with weight (which is a force). Option (C) is a distractor for those thinking of weightlessness in space, which is irrelevant here. Finally, Option (B) tests if you've reversed the logic of the Earth's shape; as noted in Physical Geography by PMF IAS, the equatorial bulge decreases gravity, so moving away from that bulge toward the poles can only result in a weight increase, never a decrease.