A brick is thrown vertically from an aircraft flying two kilometres above the earth. The brick will fall with a

1. Basics of Motion: Speed, Velocity, and Acceleration (basic)

To understand how things move, we must first distinguish between how fast they go and how that pace changes. At its simplest, speed is the distance covered by an object in a unit of time. If you know the distance and the time taken, you can calculate it using the formula: Speed = Distance / Time Science-Class VII NCERT, Measurement of Time and Motion, p.115. However, speed only tells us half the story because it doesn't mention direction. When we combine speed with a specific direction, we get velocity. For example, a train moving at 72 km/h has a specific speed, but a train moving at 72 km/h due North has a specific velocity.

In the real world, objects rarely move at the same pace forever. We distinguish between uniform motion, where an object moves at a constant speed along a straight line, and non-uniform motion, such as a car navigating city traffic where the speed constantly fluctuates Science-Class VII NCERT, Measurement of Time and Motion, p.118. This brings us to the concept of acceleration: the rate at which velocity changes. If an object is speeding up, slowing down, or changing direction, it is accelerating. If the velocity increases by the same amount every second, we call this constant (uniform) acceleration.

Concept	Definition	Key Characteristic
Speed	Distance covered per unit time.	Scalar (magnitude only).
Velocity	Speed in a specific direction.	Vector (magnitude + direction).
Acceleration	The rate of change of velocity.	Can be change in speed or direction.

A classic example of constant acceleration is free fall. When an object is dropped near the Earth's surface, the force of gravity pulls it downward. This force creates a nearly uniform acceleration due to gravity (g), which is approximately 9.8 m/s² Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306. This means that for every second an object falls, its downward speed increases by roughly 9.8 meters per second. While air resistance eventually pushes back against this fall, in fundamental mechanics, we treat the acceleration of a falling body as constant, meaning the object's speed increases at a steady, predictable rate.

Sources: Science-Class VII NCERT, Measurement of Time and Motion, p.115; Science-Class VII NCERT, Measurement of Time and Motion, p.118; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306

2. Newton's Laws of Motion (basic)

To understand how things move, we look to Sir Isaac Newton, who formulated three fundamental laws that govern the physical world. Before diving in, it is essential to know that the standard unit we use to measure force is the newton (N), named in his honor Science, Class VIII, Exploring Forces, p.65. Newton’s laws explain why a stationary car needs an engine's push to move and why a falling object, like a brick dropped from a height, speeds up as it nears the ground. Newton’s First Law (Inertia) states that an object will not change its motion unless an external force acts on it. If it’s sitting still, it stays still; if it’s moving, it keeps moving at the same speed. The Second Law (F = ma) provides the mathematical link: the force applied to an object equals its mass (the amount of matter) multiplied by its acceleration (the rate at which its speed changes). This is why, when an object falls, the Earth's gravitational pull acts as a constant force, causing the object to accelerate downward at a steady rate of approximately 9.8 m/s². This gravitational force is what we specifically call weight Science, Class VIII, Exploring Forces, p.72. Finally, the Third Law reminds us that forces never exist in isolation: for every action, there is an equal and opposite reaction. While mass is a constant property of an object, weight is a force that can change depending on where you are—for instance, you would weigh less on the Moon because the gravitational pull is weaker, even though your mass remains the same Science, Class VIII, Exploring Forces, p.77.

Concept	Mass	Weight
Definition	Amount of matter in an object.	The force of Earth's pull on the object.
Nature	Constant everywhere.	Varies by location (gravity).
SI Unit	kilogram (kg)	newton (N)

Sources: Science, Class VIII, Exploring Forces, p.65; Science, Class VIII, Exploring Forces, p.72; Science, Class VIII, Exploring Forces, p.77

3. The Universal Law of Gravitation (intermediate)

At its heart, the Universal Law of Gravitation, formulated by Sir Isaac Newton, tells us that gravity is not just a terrestrial phenomenon that makes apples fall; it is a cosmic glue. The law states that every point mass attracts every other point mass in the universe by a force pointing along the line intersecting both points. This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them (the Inverse Square Law).

When we apply this to Earth, we see its practical effects in how objects fall. Near the Earth's surface, the gravitational pull creates a nearly constant acceleration, denoted as g (approximately 9.8 m/s²). This means if you drop a heavy object, like a brick, from a height, its velocity will increase at a steady, uniform rate of 9.8 meters per second, every second. However, gravity is not perfectly uniform everywhere. Because the Earth's crust has an uneven distribution of material and mass, we encounter gravity anomalies. These variations are vital for geophysicists to understand the internal structure of our planet Physical Geography by PMF IAS, Earths Interior, p.58.

On a celestial scale, this same law governs the motion of everything from small rocky asteroids to icy comets Physical Geography by PMF IAS, The Solar System, p.35. In extreme environments, gravity can become so overwhelming that it leads to a singularity—a point where the mass is so dense that the known laws of physics break down, as seen in black holes Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.7. Today, we even use gravitational waves (ripples in spacetime) to measure the distance of moving star systems and calculate the expansion rate of our universe Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.6.

Factor	Relationship to Gravitational Force	Effect of Increasing the Factor
Mass	Directly Proportional	Force increases
Distance	Inversely Proportional (Square)	Force decreases rapidly

Sources: Physical Geography by PMF IAS, Earths Interior, p.58; Physical Geography by PMF IAS, The Solar System, p.35; Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.6-7

4. Variations in the Value of 'g' (exam-level)

While we often use the standard value of 9.8 m/s² for calculations, the acceleration due to gravity (g) is not actually a universal constant. It varies across the Earth's surface due to three primary factors: the Earth's shape, altitude, and internal mass distribution. The core formula governing this is g = GM/R², where G is the gravitational constant, M is the Earth's mass, and R is the distance from the center. This inverse relationship with the radius (R) is why 'g' changes based on where you stand.

First, consider the shape of the Earth. Our planet is not a perfect sphere but an oblate spheroid—it bulges at the equator and is flattened at the poles. Consequently, the distance from the center to the surface is greater at the equator than at the poles. Because the denominator (R) is smaller at the poles, the value of 'g' is higher at the poles and lower at the equator FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19. This means you would technically weigh slightly more at the North Pole than at the Equator!

Second, altitude plays a significant role. As you climb higher above sea level, your distance from the Earth's center of mass increases, causing 'g' to decrease. For instance, at high-altitude locations like Mana Pass (5611 m) or Thang La (5359 m), the gravitational pull is slightly weaker than at the coast Geography of India, Majid Husain, Physiography, p.21-22. Finally, the Earth's crust is not uniform. Dense mineral deposits or mountain ranges can create a gravity anomaly, where the measured gravity differs from the expected value due to the uneven distribution of mass within the crust FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19.

Factor	Change in Position	Effect on 'g'
Latitude	Moving from Equator to Poles	Increases (Radius decreases)
Altitude	Moving from Sea Level to Mountain Top	Decreases (Distance from center increases)
Mass Distribution	Region with high-density materials	Increases (Gravity Anomaly)

Sources: FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19; Geography of India, Majid Husain (9th ed.), Physiography, p.21-22

5. Mass, Weight, and Weightlessness (intermediate)

To master mechanics, we must first clear a common confusion: the difference between mass and weight. In everyday conversation, we use them interchangeably, but in science, they represent two very different physical realities. Mass is the measure of the quantity of matter present in an object. It is an intrinsic property, meaning it does not change regardless of where you are in the universe. Whether you are on Earth, the Moon, or floating in deep space, your mass remains the same, measured in kilograms (kg) Science Class VIII NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.142.

Weight, on the other hand, is not a property of the object alone; it is a force. Specifically, it is the gravitational force with which a celestial body (like Earth) pulls an object toward itself. Because weight depends on gravity, it varies from place to place. For instance, because the Moon's gravity is weaker than Earth's, you would weigh much less there, even though your mass hasn't changed a bit Science Class VIII NCERT, Exploring Forces, p.75. Weight is measured in Newtons (N), often using tools like a spring balance, which measures the stretch caused by this gravitational pull Science Class VIII NCERT, Exploring Forces, p.74.

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Gravitational force acting on an object.
Nature	Constant everywhere.	Changes with gravitational field strength.
SI Unit	Kilogram (kg).	Newton (N).

Finally, let's touch upon weightlessness. This is a state where the apparent weight of an object becomes zero. It doesn't mean gravity has disappeared! Instead, it happens when an object is in free fall—meaning it is falling under the influence of gravity with no support force (like a floor) pushing back against it. Astronauts in orbit, like India's first cosmonaut Rakesh Sharma, experience this state continuously while circling the Earth Rajiv Ahir, A Brief History of Modern India, After Nehru, p.715. In this state, even though the Earth is still pulling on them (gravity is present), they feel weightless because they and their spacecraft are falling together at the same rate.

Sources: Science Class VIII NCERT, Exploring Forces, p.74; Science Class VIII NCERT, Exploring Forces, p.75; Science Class VIII NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.142; Rajiv Ahir, A Brief History of Modern India, After Nehru..., p.715

6. Motion Under Gravity: Free Fall (intermediate)

Welcome to Hop 6! We are moving into one of the most elegant parts of mechanics: Free Fall. In physics, an object is said to be in free fall when it moves solely under the influence of the Earth's gravitational pull. While we often think of "falling" as moving downward, in a scientific sense, even an object thrown upward is in "free fall" the moment it leaves your hand, because only gravity is dictating its acceleration.

Gravity is a non-contact, attractive force exerted by the Earth on all objects Science, Class VIII NCERT, Exploring Forces, p.72. Near the Earth's surface, this force produces a constant acceleration, denoted as g. For most calculations, we take g to be approximately 9.8 m/s² Physical Geography by PMF IAS, The Solar System, p.23. This means that for every second an object falls, its velocity increases by exactly 9.8 meters per second. This uniform acceleration is independent of the object's mass; in a vacuum, a feather and a brick would hit the ground at the exact same time.

However, as a civil services aspirant, you must realize that g is not perfectly uniform everywhere on Earth. Its value varies based on two primary factors:

• Latitude: Gravity is greater at the poles and less at the equator because the Earth is an oblate spheroid (the equator is further from the center than the poles) Fundamentals of Physical Geography, Geography Class XI NCERT, The Origin and Evolution of the Earth, p.19.
• Mass Distribution: Local variations in the density of materials within the Earth's crust can cause the observed gravity to differ from the expected value—a phenomenon known as a gravity anomaly Fundamentals of Physical Geography, Geography Class XI NCERT, The Origin and Evolution of the Earth, p.19.

In practical scenarios, like the debris fall seen in landslides where earth materials drop from a vertical face, we treat the movement as nearly free fall Fundamentals of Physical Geography, Geography Class XI NCERT, Geomorphic Processes, p.42. While air resistance eventually slows down very light objects, for dense objects (like a rock or a brick), we assume the acceleration remains constant throughout the descent for all standard mechanical problems.

Body	Surface Gravity (m/s²)	Comparison to Earth
Sun	274	~28 times
Earth	9.8	1 time
Moon	1.62	~1/6th

Sources: Science, Class VIII NCERT, Exploring Forces, p.72; Physical Geography by PMF IAS, The Solar System, p.23; Fundamentals of Physical Geography, Geography Class XI NCERT, The Origin and Evolution of the Earth, p.19; Fundamentals of Physical Geography, Geography Class XI NCERT, Geomorphic Processes, p.42

7. Air Resistance and Terminal Velocity (exam-level)

When an object is dropped from a height, it moves vertically downward under the influence of gravity. In a vacuum, this object would accelerate indefinitely at a constant rate of approximately 9.8 m/s², known as 'g'. However, in our atmosphere, the air itself acts as a fluid that resists this motion. This opposing force is known as Air Resistance (or Drag). As the object gains speed, the air molecules collide with it more frequently and with greater force, meaning air resistance is directly proportional to the object's velocity.

As the object continues to fall, the upward force of air resistance increases until it eventually equals the downward pull of gravity. At this precise moment, the net force acting on the object becomes zero. According to Newton’s Laws, when there is no net force, there is no acceleration. The object stops speeding up and continues to fall at a constant, maximum speed known as Terminal Velocity. While we often assume constant acceleration for heavy, dense objects like a brick for simplicity Science Class VIII NCERT, Exploring Forces, p.72, in reality, every falling object in the atmosphere is subject to these fluid dynamics.

Stage of Fall	Force Balance	Motion Status
Initial Drop	Gravity > Air Resistance	Accelerating (Speeding up)
Mid-Fall	Gravity > Air Resistance (but Drag is increasing)	Accelerating (but rate of acceleration is decreasing)
Terminal Velocity	Gravity = Air Resistance	Constant Velocity (Zero acceleration)

Factors like surface area and shape significantly influence how quickly an object reaches terminal velocity. For instance, a skydiver increases their air resistance by spreading their limbs to slow down. Similarly, in geography, we see that the movement of air (wind) is affected by various factors, including friction and pressure gradient forces, which dictate how air masses interact with the Earth's surface Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306.

Sources: Science Class VIII NCERT, Exploring Forces, p.72; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306

8. Solving the Original PYQ (exam-level)

This question serves as a practical application of the Kinematics and Newtonian Mechanics concepts you have just covered. To solve this, you must synthesize the relationship between force, mass, and acceleration. When the brick is released at a height of two kilometers, it enters a state of free fall. According to Newton’s Second Law ($F = ma$), a constant force results in a constant acceleration. Because the Earth exerts a nearly uniform gravitational pull (approximately $9.8 m/s^2$) on the brick throughout its descent, the rate at which its velocity changes remains steady. Therefore, the brick falls with (C) constant acceleration.

As a student of the UPSC, you must be wary of the "real-world vs. ideal-world" trap. While air resistance exists in reality, standard physics problems involving dense objects like bricks assume an idealized vacuum-like environment unless stated otherwise. This is why options (A) and (B) are incorrect; constant speed or constant velocity would imply that no net force is acting on the brick, which contradicts the presence of gravity. Reasoning through the forces is key: if gravity is the only significant force, acceleration must be the constant factor, not the speed.

UPSC frequently uses Option (D) as a distractor to tempt students into overthinking fluid dynamics and terminal velocity. However, even if air resistance were considered, an object would start with constant acceleration and eventually reach a constant speed (terminal velocity)—the reverse of what Option D suggests. By sticking to the core principle that acceleration due to gravity (g) is uniform near the Earth's surface, as discussed in NASA: Motion of a Free-Falling Object, you can confidently navigate these conceptual hurdles.

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