Consider the following statements 1. A rubber ball bounces higher at the equator than at the poles. 2. When two persons walk on the moon, they hear each other with lower frequency. Which of the statements given above is/ are correct ?

1. Fundamentals of Gravitation and 'g' (basic)

Welcome to your first step in mastering mechanics! To understand why things fall or why planets stay in orbit, we must start with the Universal Law of Gravitation. Proposed by Isaac Newton, this theory was the climax of the scientific revolution Themes in world history, History Class XI (NCERT 2025 ed.), Changing Cultural Traditions, p.119. At its heart, gravitation is an attractive force that exists between any two objects with mass. The magnitude of this force depends on two things: how heavy the objects are and how far apart they are. In physics, we measure this force in Newtons (N) Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.65.

While gravitation is the force, 'g' (acceleration due to gravity) is the rate at which an object speeds up when it falls toward a planet. On Earth, we often treat g as a constant (9.8 m/s²), but it actually varies across the globe. This is 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. Since the equator is further from the Earth's center than the poles are, the pull of gravity is slightly weaker there. Furthermore, the Earth's rotation creates a centrifugal force that acts outward, effectively reducing the net gravitational pull at the equator even more.

Location	Distance from Center	Value of 'g'	Weight of an Object
Poles	Shorter	Maximum	Heavier
Equator	Longer	Minimum	Lighter

Interestingly, the value of gravity isn't just affected by shape. The uneven distribution of mass within the Earth's crust — like dense metallic ores or deep ocean trenches — causes small local variations known as gravity anomalies Physical Geography by PMF IAS, Earths Interior, p.58. These anomalies are vital for geologists because they provide clues about what lies beneath the Earth's surface without having to drill deep holes.

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

2. Nature of Sound and Wave Propagation (basic)

To understand the nature of sound, we must first recognize it as a mechanical wave. Unlike light, which is an electromagnetic wave and can travel through the void of a vacuum, sound is entirely dependent on a material medium—be it solid, liquid, or gas—to propagate. This is because sound travels by physically disturbing particles; it relies on the interaction of molecules to pass energy from one point to another. In a vacuum, such as the lunar surface or outer space, there are no particles to vibrate, making it impossible for sound to travel Physical Geography by PMF IAS, Earths Atmosphere, p.278.

The mechanism of sound propagation involves the compression and rarefaction of the medium. As a sound source vibrates, it pushes nearby molecules together (compression) and then creates a space for them to spread out (rarefaction). This movement is longitudinal, meaning the particles of the medium vibrate parallel to the direction the wave is traveling. This is very similar to how P-waves (Primary waves) behave during an earthquake, creating density differences as they stretch and squeeze the rock material FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Chapter 2, p.20.

Interestingly, the speed of sound is not constant; it changes based on the properties of the medium. Generally, sound travels faster in solids than in liquids, and faster in liquids than in gases. This is because a higher density often leads to greater elasticity, allowing the particles to return to their original positions more quickly after being disturbed. While light slows down when entering a denser medium like glass (due to a higher refractive index), sound actually thrives in denser, more elastic environments Physical Geography by PMF IAS, Earths Magnetic Field (Geomagnetic Field), p.64.

Feature	Sound Waves	Light Waves
Type	Mechanical (Longitudinal)	Electromagnetic (Transverse)
Medium	Requires a medium (cannot travel in vacuum)	Does not require a medium
Speed in denser media	Generally increases	Decreases (higher refractive index)

Sources: Physical Geography by PMF IAS, Earths Atmosphere, p.278; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Chapter 2: The Origin and Evolution of the Earth, p.20; Physical Geography by PMF IAS, Earths Magnetic Field (Geomagnetic Field), p.64

3. Earth's Shape: The Oblate Spheroid (basic)

While we often visualize Earth as a perfect marble, it is actually an oblate spheroid (sometimes referred to as a Geoid). This means the Earth is slightly flattened at the poles and features a distinct bulge at the equator. Think of it like a soft rubber ball that is being slightly squeezed from the top and bottom. This shape isn't accidental; it is a direct consequence of the Earth's rotation on its axis Physical Geography by PMF IAS, Latitudes and Longitudes, p.241.

As the Earth spins, it generates a centrifugal force—the same outward-tugging sensation you feel when a car takes a sharp turn. Because the Earth's rotational speed is highest at the equator and effectively zero at the poles, this force pulls the Earth's mass outward most strongly at the center. Over millions of years, this has resulted in an equatorial bulge. This concept is so fundamental that Alfred Wegener even cited this "pole-fleeing force" (the centrifugal force directed away from the poles) as one of the drivers behind the movement of entire continents Fundamentals of Physical Geography (NCERT), Interior of the Earth, p.28.

This "imperfect" shape has a massive impact on the acceleration due to gravity (g). Because of the bulge, the equator is further away from the Earth's center than the poles are. Since the pull of gravity weakens as distance from the center increases, the gravitational force is stronger at the poles and weaker at the equator Physical Geography by PMF IAS, Latitudes and Longitudes, p.241. This means you would actually weigh slightly more at the North Pole than you would at the Equator!

Feature	At the Equator	At the Poles
Distance from Center	Greater (due to bulge)	Smaller (flattened)
Centrifugal Force	Maximum	Zero
Gravity (g)	Lower	Higher

Sources: Physical Geography by PMF IAS, Latitudes and Longitudes, p.241; Fundamentals of Physical Geography (NCERT), Interior of the Earth, p.28

4. Atmospheric Science: Why the Moon is a Vacuum (intermediate)

To understand why the Moon is a vacuum, we must look at the balance between gravitational pull and molecular energy. For a celestial body to hold an atmosphere, its gravity must be strong enough to keep gas molecules from flying away into space. On the Moon, the acceleration due to gravity is only about 1/6th of that on Earth. This results in a very low escape velocity — the minimum speed an object needs to break free from a planet's gravity. While Earth's escape velocity is approximately 11.2 km/s, the Moon's is only about 2.4 km/s. At daytime temperatures, even relatively heavy gas molecules can reach speeds exceeding this limit and simply drift away into the void Physical Geography by PMF IAS, Earths Atmosphere, p.280.

Beyond gravity, the lack of a protective magnetic field plays a critical role. Earth is shielded by a strong magnetic dipole that deflects the solar wind — a stream of charged particles from the Sun. The Moon, however, has a very weak magnetic field and no dipole. Without this shield, the solar wind slams directly into the lunar surface, a process called atmospheric stripping. This constant "sandblasting" by solar particles ensures that any gases released from the interior or brought by comets are quickly swept out into space Physical Geography by PMF IAS, Earths Magnetic Field (Geomagnetic Field), p.69.

The consequences of this vacuum are profound for the lunar environment. Because there is no air to act as a medium, sound waves (which are mechanical waves) cannot propagate; two astronauts on the Moon cannot hear each other speak through the environment. Furthermore, without an atmosphere to trap heat or block radiation, the Moon experiences extreme temperature swings, ranging from 127 °C in the sun to −173 °C in the shade, and is constantly bombarded by meteors that would otherwise burn up in an atmosphere Physical Geography by PMF IAS, The Solar System, p.27, 29.

Feature	Earth	Moon
Gravity	Strong (9.8 m/s²)	Weak (~1.6 m/s²)
Magnetic Field	Strong Dipole (Shields atmosphere)	Negligible (No shield)
Atmospheric Result	Dense, life-sustaining	Near-vacuum (Exosphere only)

Sources: Physical Geography by PMF IAS, Earths Atmosphere, p.280; Physical Geography by PMF IAS, Earths Magnetic Field (Geomagnetic Field), p.69; Physical Geography by PMF IAS, The Solar System, p.27; Physical Geography by PMF IAS, The Solar System, p.29

5. Spatial Variation of Gravity (Latitude and Rotation) (intermediate)

While we often simplify the acceleration due to gravity (g) as a constant 9.8 m/s², it actually varies across the Earth's surface. This spatial variation is not random; it follows a predictable pattern based on latitude. If you were to weigh yourself at the Equator and then at the North Pole using a highly sensitive scale, you would find you are 'heavier' at the Pole. This happens because the Earth is not a perfect sphere but a Geoid (or oblate spheroid) — it is slightly flattened at the poles and bulges at the equator Physical Geography by PMF IAS, Latitudes and Longitudes, p.241.

Two primary factors drive this difference:

• The Shape Factor: Because of the equatorial bulge, the distance from the Earth's center to the surface is greater at the Equator than at the poles. Since gravity follows an inverse-square relationship with distance (g ∝ 1/r²), the pull is naturally weaker where the radius is larger FUNDAMENTALS OF PHYSICAL GEOGRAPHY (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19.
• The Rotation Factor: As the Earth rotates on its axis, it generates centrifugal force that acts outward, away from the center. This force is at its maximum at the Equator (where rotational speed is highest) and effectively zero at the poles. Because centrifugal force acts in the opposite direction to gravity, it 'cancels out' a small portion of the gravitational pull at the Equator Physical Geography by PMF IAS, Latitudes and Longitudes, p.241.

Beyond these large-scale patterns, local variations also exist. The mass distribution within the Earth's crust is uneven; for instance, areas with dense ore deposits exert a slightly stronger pull than areas with less dense material. Scientists refer to the difference between the observed gravity and the expected theoretical value as a gravity anomaly FUNDAMENTALS OF PHYSICAL GEOGRAPHY (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19.

Feature	At the Equator (0°)	At the Poles (90°)
Distance from Earth's Center	Maximum (Radius is larger)	Minimum (Radius is smaller)
Centrifugal Force	Maximum	Zero
Value of 'g'	Minimum	Maximum

Sources: Physical Geography by PMF IAS, Latitudes and Longitudes, p.241; FUNDAMENTALS OF PHYSICAL GEOGRAPHY (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19

6. Mechanics of Bouncing and Projectile Motion (exam-level)

To understand why an object—like a cricket ball—bounces differently in different locations, we must first look at the forces acting on a projectile. When you throw a ball upward, it doesn't maintain a constant speed. As highlighted in Science, Class VIII, Exploring Forces, p.78, the ball slows down during its upward motion, momentarily stops at the highest point, and then accelerates downward. This entire journey is governed by the acceleration due to gravity (g), which acts vertically downward at all times. From a first-principles perspective, the maximum height (h) a ball reaches for a given initial velocity (u) is determined by the formula h = u² / 2g. This tells us a critical secret: Height is inversely proportional to gravity. If 'g' decreases, the ball will travel higher.

So, why would 'g' change? The Earth is not a perfect sphere but an oblate spheroid, meaning it bulges at the middle. According to Fundamentals of Physical Geography, Class XI, The Origin and Evolution of the Earth, p.19, the distance from the Earth's center to the surface is greater at the equator than at the poles. Since gravity's pull weakens as you move further from the center of mass, the value of 'g' is minimum at the equator and maximum at the poles. Furthermore, the Earth's rotation creates a centrifugal force that pushes outward most strongly at the equator, effectively 'canceling' a tiny fraction of gravity. Because the net gravity is lower at the equator, a ball hit or bounced with the same energy will reach a greater height there than it would at the North or South Pole.

Feature	At the Equator	At the Poles
Distance from Earth's Center	Greater (Equatorial Bulge)	Smaller
Centrifugal Force	Maximum	Zero
Value of Gravity (g)	Lower	Higher
Bounce Height (h)	Higher	Lower

Sources: Science, Class VIII (Revised ed 2025), Exploring Forces, p.78; Fundamentals of Physical Geography, Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19

7. Solving the Original PYQ (exam-level)

This question beautifully synthesizes two core pillars of general science you've just mastered: gravitational dynamics and the physics of wave propagation. To solve this, you must apply the principle of Earth's non-spherical shape to Statement 1 and the necessity of a medium for mechanical waves to Statement 2. It’s a classic example of how UPSC tests your ability to translate theoretical building blocks into physical scenarios.

Walking through the reasoning, we first look at the acceleration due to gravity (g). As noted in FUNDAMENTALS OF PHYSICAL GEOGRAPHY (NCERT Class XI) and Physical Geography by PMF IAS, Earth is an oblate spheroid, meaning the equator is further from the center than the poles. This equatorial bulge, combined with maximum centrifugal force at the equator, results in a lower value of 'g' at the equator. Because the downward pull is weaker, a ball is less restricted in its upward movement, leading to a higher bounce. Conversely, Statement 2 is a conceptual trap. While the Moon has gravity, it lacks a significant atmosphere. Since sound is a mechanical wave, it requires a medium to travel; in the vacuum of the lunar surface, sound cannot propagate at all. Therefore, the two persons would hear nothing, not a 'lower frequency.'

The correct answer is (A) 1 only. UPSC often uses distractor terminology like "lower frequency" in Statement 2 to tempt students who might confuse the Moon's lower gravity with its atmospheric conditions. Options (B) and (C) are common traps designed to catch those who over-generalize the effects of the lunar environment. By strictly applying the rule that sound cannot travel in a vacuum, you can confidently eliminate any option suggesting sound is heard at any frequency, leaving only the correct gravitational logic for Statement 1.