Statement I : A body weighs less on a hill top than on earth’s surface even though its mass remains unchanged. Statement I : The acceleration due to gravity of the earth decreases with height.

1. Newton's Law of Universal Gravitation (basic)

At the heart of classical mechanics lies Newton’s Law of Universal Gravitation, a concept that fundamentally changed our understanding of the cosmos by proving that the same rules apply to a falling apple and the orbiting moon History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119. This law states that every object in the universe attracts every other object 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. Formally, this is expressed as F = G · (m₁ · m₂) / r², where G is the Universal Gravitational Constant, m represents mass, and r is the distance between the two bodies.

In our daily lives, we experience this most prominently as gravity—the force with which the Earth attracts objects toward itself Science, Class VIII (NCERT 2025 ed.), Exploring Forces, p.72. Unlike magnetic or electrostatic forces, which can both attract and repel, gravitational force is strictly attractive. It is also a non-contact force, meaning it acts across space without requiring physical touch between the Earth and the object Science, Class VIII (NCERT 2025 ed.), Exploring Forces, p.72. The strength of this pull (measured in Newtons, symbol N) depends heavily on the mass involved; for instance, the uneven distribution of mass within the Earth’s crust leads to slight variations in gravity known as gravity anomalies Physical Geography by PMF IAS, Earths Interior, p.58.

Crucially, because the force is inversely proportional to the square of the distance (r²), even a small increase in distance leads to a significant drop in gravitational pull. This "inverse-square law" explains why the Earth's pull weakens as you move further into space or even to high altitudes. As mass increases, the force increases; as distance increases, the force decreases rapidly.

Feature	Gravitational Force	Magnetic/Electrostatic Force
Nature	Always attractive	Can be attractive or repulsive
Contact	Non-contact (acts at a distance)	Non-contact
Dependence	Mass and Distance	Charge/Pole strength and Distance

Sources: History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119; Science, Class VIII (NCERT 2025 ed.), Exploring Forces, p.72; Science, Class VIII (NCERT 2025 ed.), Exploring Forces, p.65; Physical Geography by PMF IAS, Earths Interior, p.58

2. Distinguishing Mass and Weight (basic)

In our daily lives, we often use the terms 'mass' and 'weight' interchangeably. If you buy a 10 kg bag of rice, you might say its 'weight' is 10 kg. However, in the world of physics—and for your UPSC preparation—distinguishing between these two is vital. They represent two fundamentally different properties of matter.

Mass is defined as the quantity of matter present in an object or substance Science, Class VIII, Chapter 9, p.142. Think of it as a measure of 'how much stuff' is inside an object. Because the amount of matter doesn't change based on where you go, mass is a constant property. Whether you are standing on the Equator, at the North Pole, or floating on the International Space Station, your mass remains exactly the same.

Weight, on the other hand, is a force. Specifically, it is the gravitational force with which a planet (like Earth) pulls an object toward itself Science, Class VIII, Chapter 5, p.75. Because weight depends on the strength of gravity, it is variable. The relationship is expressed by the formula: W = mg (where 'm' is mass and 'g' is the acceleration due to gravity). If 'g' changes, your weight changes, even if your mass stays identical.

For example, if you travel to the Moon, your mass remains the same because you are made of the same amount of 'matter.' However, because the Moon's gravity is much weaker than Earth's, your weight would be significantly less Science, Class VIII, Chapter 5, p.75. Similarly, as you move to a hilltop or high altitude, you are getting slightly further away from the Earth's center. This increase in distance causes the gravitational pull ('g') to decrease slightly, making you weigh a tiny bit less at the top of a mountain than at sea level.

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Force of gravitational attraction.
Nature	Intrinsic property (Constant).	Extrinsic property (Variable).
SI Unit	kilogram (kg)	newton (N)
Measurement Tool	Two-pan balance (comparison).	Spring balance Science, Class VIII, Chapter 5, p.74.

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.74, 75, 77

3. Acceleration due to Gravity (g) on Earth (basic)

At its simplest, acceleration due to gravity (g) is the rate at which an object speeds up as it falls toward Earth, solely under the influence of Earth's gravitational pull. On the surface, this value is approximately 9.8 m/s². However, it is vital to distinguish between mass (the amount of matter in an object) and weight. Weight is actually a force, calculated as the product of mass and gravity: W = mg Science, Class VIII (NCERT), Chapter 5, p.75. While your mass remains constant wherever you go in the universe, your weight can change depending on the local value of g.

Why does g change? The strength of gravity depends on how far you are from the center of the Earth. Specifically, gravity is inversely proportional to the square of the distance from the Earth's center. This means as you move further away—such as climbing a high mountain or flying in a balloon—the distance increases, and the value of g decreases. Consequently, an object will weigh slightly less on a hilltop than it does at sea level because the gravitational pull is weaker at higher altitudes.

Interestingly, Earth is not a perfect sphere; it is an "oblate spheroid," meaning it bulges at the equator and is flattened at the poles. Because of this shape, the distance from the center at the equator is greater than at the poles. As a result, the value of gravity is greater near the poles and less at the equator Fundamentals of Physical Geography, Geography Class XI (NCERT), Chapter 2, p.19. Beyond just shape, the density of materials beneath your feet also matters. Uneven distribution of mass within the Earth's crust causes slight variations in gravity readings, a phenomenon scientists call a gravity anomaly Physical Geography by PMF IAS, Earths Interior, p.58.

Sources: Science, Class VIII (NCERT), Chapter 5: Exploring Forces, p.75; Fundamentals of Physical Geography, Geography Class XI (NCERT), Chapter 2: The Origin and Evolution of the Earth, p.19; Physical Geography by PMF IAS, Earths Interior, p.58

4. Earth's Shape and Gravity Variation (intermediate)

To understand why things weigh differently in different places, we must first distinguish between mass and weight. Mass is the intrinsic amount of matter in an object and remains constant regardless of location. Weight, however, is the gravitational force exerted by the Earth on that mass, calculated as W = mg. Because the acceleration due to gravity (g) is not uniform across the globe, your weight actually changes as you move from the equator to the poles or climb a mountain. Why does g vary? This is primarily due to the Earth's shape, which is not a perfect sphere but a Geoid (or oblate spheroid). Because the Earth rotates, centrifugal force causes it to bulge at the equator and flatten at the poles. Consequently, the distance from the Earth's center to the surface is greater at the equator than at the poles Physical Geography by PMF IAS, Latitudes and Longitudes, p.241. Since gravity follows an inverse-square law—meaning it gets weaker as you move further from the center—the value of g is lowest at the equator and highest at the poles Fundamentals of Physical Geography, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19. Similarly, altitude plays a role. When you stand on a hilltop, your distance from the Earth's center (the radius R plus your height h) increases. This increased distance results in a slight decrease in the pull of gravity, making you weigh marginally less than you would at sea level. Beyond just distance, the actual distribution of mass within the Earth’s crust is uneven. Scientists refer to the difference between the observed gravity and the expected value as a gravity anomaly, which helps us map different materials inside the Earth Physical Geography by PMF IAS, Earths Interior, p.58.

Location	Distance from Center	Value of Gravity (g)	Your Weight
Poles	Shorter (Flattened)	Higher	Maximum
Equator	Longer (Bulged)	Lower	Minimum
High Altitude	Increased (R + h)	Decreased	Lowered

Sources: 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; Physical Geography by PMF IAS, Earths Interior, p.58

5. Connected Concept: Weightlessness and Satellites (intermediate)

To understand weightlessness, we must first distinguish between mass and weight. Mass is the intrinsic amount of matter in an object and remains constant regardless of location Science, Class VIII. NCERT, Exploring Forces, p.75. Weight, however, is the gravitational force exerted by the Earth on that mass, calculated as W = mg. Because weight depends on the acceleration due to gravity (g), it is not a fixed value. The value of 'g' is inversely proportional to the square of the distance from the Earth’s center; therefore, as you move to a higher altitude—like a hilltop—the distance from the Earth's center increases, causing 'g' to decrease and your weight to drop slightly.

When we discuss weightlessness in satellites, a common misconception is that gravity is absent in space. In reality, gravity at the altitude of the International Space Station is still about 90% of what it is on the surface! The sensation of weightlessness occurs because the satellite and the astronauts inside are in a state of sustained free fall. They are moving forward at such a high velocity that as they fall toward Earth, the Earth curves away beneath them. Since the spacecraft and the occupant are falling at the same rate, there is no reaction force (normal force) from the floor, making the occupant feel weightless.

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Force of gravity acting on an object.
Constancy	Constant everywhere in the universe.	Varies based on location and altitude.
Measurement	Measured in kg (using a beam balance).	Measured in Newtons (using a spring balance).

Satellites are typically placed in high orbits, such as the exosphere, where the air is so thin that atmospheric drag is negligible Physical Geography by PMF IAS, Earths Atmosphere, p.280. This allows them to maintain the high speeds necessary to stay in orbit for years. India uses specialized launch vehicles like the PSLV (Polar Satellite Launch Vehicle) and GSLV (Geosynchronous Satellite Launch Vehicle) to transport these payloads into their specific orbital paths Geography of India, Majid Husain, Transport, Communications and Trade, p.58.

Sources: Science, Class VIII. NCERT, Exploring Forces, p.75; Physical Geography by PMF IAS, Earths Atmosphere, p.280; Geography of India, Majid Husain, Transport, Communications and Trade, p.58

6. Variation of 'g' with Altitude (Height) (exam-level)

To understand why gravity changes as we go higher, we must start with the fundamental nature of Earth's pull. Acceleration due to gravity (g) is not a universal constant; rather, it is a value that depends heavily on how far you are from the Earth's center of mass. Gravity is the force that keeps us in contact with the surface and drives all geomorphic processes, such as the movement of water or soil from higher to lower levels FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Geomorphic Processes, p.38. Specifically, the value of 'g' is inversely proportional to the square of the distance from the center of the Earth. This means as the distance increases, the gravitational pull weakens significantly.

Imagine standing at sea level (the Earth's surface). You are at a distance 'R' (the Earth's radius) from the center. If you climb a high mountain or fly in an aircraft to a height 'h', your total distance from the center becomes (R + h). Since the denominator in our gravity calculation is now larger, the resulting value of 'g' decreases. Consequently, your weight—which is the force of gravity acting on your mass (W = mg)—will also decrease as you reach higher altitudes. It is important to distinguish between mass and weight in this context:

Feature	Mass (m)	Weight (W)
Definition	The amount of matter in an object.	The gravitational force exerted on an object.
Effect of Altitude	Constant: It remains the same whether you are on a hilltop or the beach.	Variable: It decreases as altitude increases because 'g' decreases.

Interestingly, this variation in gravity is part of why the Earth is not a perfect sphere. Gravity is stronger at the poles because they are closer to the Earth's center than the equator FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19. When we combine this with altitude, we see that a person will technically weigh slightly less at the summit of a mountain at the equator than at a sea-level beach at the poles.

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

7. Solving the Original PYQ (exam-level)

This question perfectly synthesizes the fundamental concepts of gravitational force and the distinction between mass and weight. Having just learned that mass is an intrinsic property that remains constant, you can see Statement I as a practical application of the universal formula W = mg. The core of this problem lies in understanding that while mass (m) is invariant, weight (W) is a force that fluctuates based on the acceleration due to gravity (g) at a specific location, a distinction emphasized in Science, Class VIII. NCERT (Revised ed 2025).

To arrive at the correct answer, (A), your reasoning should follow a logical chain: first, recognize that moving to a hilltop increases the distance from the Earth's center; second, apply the physical principle that g decreases as height increases; and third, conclude that a lower g directly results in a lower weight. Statement II provides the scientific "why" behind the observation in Statement I, creating a clear causal link. As explained in NASA: Beginner’s Guide to Aeronautics, weight depends directly on the local strength of gravity, which weakens as you move further from the planetary mass.

UPSC often uses Option (B) as a trap, where both statements are scientifically true but lack a direct cause-and-effect relationship. In this case, however, Statement II is the direct physical explanation for Statement I, making (A) the correct choice. Common mistakes include treating mass as variable or forgetting the inverse square relationship between gravity and distance. Always test these questions by placing the word "because" between the two statements; if the logic remains sound, Statement II is the correct explanation.