If a small raindrop falls through air

1. Newton’s Second Law and Net Force (basic)

To understand how everything from a falling apple to a launching rocket moves, we must start with Newton’s Second Law of Motion. This law provides the mathematical link between force, mass, and motion. It states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. We express this with the fundamental formula: Force = mass × acceleration (F = ma). The standard unit for measuring this interaction is the newton (N) Science ,Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.65.

In a laboratory, we might imagine a single force acting on an object, but in the real world, objects are usually subject to multiple forces simultaneously. To predict motion, we must calculate the Net Force. Think of the word "net" just as you would in ecology or economics: just as Net Primary Production (NPP) is the energy remaining after accounting for respiration losses Environment and Ecology, Majid Hussain (Access publishing 3rd ed.), BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.33, Net Force is the resultant "leftover" force acting on an object after adding up all the individual forces (like gravity, friction, or muscular force) acting in different directions.

If the forces acting on an object are perfectly balanced, the Net Force is zero. According to Newton's law (F = ma), if the force is zero, the acceleration must also be zero. This leads to two possible states for the object:

• It remains at rest (if it was already stationary).
• It moves at a constant velocity (if it was already moving).

A practical example of this is a raindrop or a fruit falling from a tree Science ,Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.77. Initially, the force of gravity is greater than air resistance, so the object accelerates. However, as it speeds up, air resistance increases until it exactly matches the pull of gravity. At this point, the Net Force becomes zero, and the object stops accelerating, continuing to fall at a steady pace known as terminal velocity.

Sources: Science ,Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.65; Science ,Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.77; Environment and Ecology, Majid Hussain (Access publishing 3rd ed.), BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.33

2. Gravity and Free Fall in a Vacuum (basic)

To understand mechanics, we must first look at Gravity—the invisible pull that keeps our feet on the ground and governs the movement of everything from planets to pebbles. On Earth, gravity acts as a constant downward force that drives all geomorphic processes, such as the flow of water and the movement of soil FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Geomorphic Processes, p.38. The strength of this pull is measured as acceleration due to gravity (g), which on Earth averages about 9.8 m/s² Physical Geography by PMF IAS, The Solar System, p.23.

Free fall occurs when an object falls solely under the influence of gravity, with no other forces (like air resistance) acting upon it. In our everyday experience, a leaf falls slower than a stone because of air. However, in a vacuum (a space with no air), a revolutionary principle emerges: all objects fall at the exact same rate regardless of their mass or shape. This is because gravity accelerates every kilogram of mass by the same 9.8 m/s² every second. As a result, an object in free fall is in non-uniform linear motion, meaning its speed is not constant but increases steadily as it descends Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.117.

Feature	Fall in Atmosphere (Air)	Fall in a Vacuum
Forces Acting	Gravity + Air Resistance (Drag)	Gravity only
Rate of Fall	Depends on shape and mass	Identical for all objects
Acceleration	Decreases as speed increases	Constant (approx. 9.8 m/s²)

It is important to note that gravity is not perfectly uniform everywhere on Earth. It is greater near the poles and less at the equator because the Earth is not a perfect sphere; the poles are closer to the center of mass FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19. This variation is known as a gravity anomaly, and it reminds us that while 'g' is a constant in our basic equations, the physical world has fascinating nuances.

Sources: FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Geomorphic Processes, p.38; Physical Geography by PMF IAS, The Solar System, p.23; Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.117; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19

3. Buoyancy and Upthrust in Fluids (intermediate)

When you try to push an empty plastic bottle into a bucket of water, you feel a distinct resistance pushing back against your hand. This upward force exerted by a fluid (liquid or gas) on any object immersed in it is known as upthrust or buoyant force Science, Class VIII, Exploring Forces, p.77. This phenomenon isn't restricted to water; it is a fundamental property of all fluids, including the air around us. In fact, the very reason a hot air balloon rises is because the air it displaces is heavier than the balloon itself, creating a net upward push. To understand the strength of this force, we look to Archimedes' Principle. It states that when an object is fully or partially submerged in a fluid, the upward buoyant force is exactly equal to the weight of the fluid displaced by the object Science, Class VIII, Exploring Forces, p.76. This principle explains why a massive steel ship can float while a tiny iron nail sinks: the ship is designed to be hollow, allowing it to displace a volume of water that weighs as much as the ship itself. Whether an object sinks or floats is ultimately a "tug-of-war" between two opposing forces: the downward gravitational force (weight) and the upward buoyant force. If the weight of the object is greater than the weight of the fluid it displaces, it sinks. If they are equal, the object floats Science, Class VIII, Exploring Forces, p.76. Additionally, the density of the fluid plays a crucial role; for example, it is easier to float in the highly saline Dead Sea than in a freshwater lake because saltwater is denser and provides a greater buoyant force for the same volume displaced.

Scenario	Force Comparison	Result
Weight > Buoyant Force	Downward pull is stronger	Object Sinks
Weight = Buoyant Force	Forces are balanced	Object Floats
Weight < Buoyant Force	Upward push is stronger	Object rises to the surface

Sources: Science, Class VIII, Exploring Forces, p.76; Science, Class VIII, Exploring Forces, p.77

4. Viscosity and Fluid Friction (intermediate)

When we think of friction, we usually imagine two solid surfaces rubbing together, like your shoes on the pavement. However, friction also exists within fluids (liquids and gases). Viscosity is essentially the "internal friction" of a fluid; it represents a fluid's resistance to flow or change in shape. Imagine pouring honey versus pouring water—the honey is much more viscous because its internal layers strongly resist sliding past one another.

When an object moves through a fluid, it experiences Fluid Friction, often called Drag. This force acts in the opposite direction of the object's motion. The magnitude of this drag depends on several factors: the speed of the object, its shape, and the viscosity of the fluid. In the upper atmosphere, for instance, at altitudes of 2-3 km, the air is thin and far enough from the Earth's surface that winds are considered "free from the frictional effect of the surface." Without this surface friction to slow them down, forces like the Coriolis force and pressure gradients reach a unique balance, resulting in what we call geostrophic winds Physical Geography by PMF IAS, Jet streams, p.384.

A classic application of these principles is the phenomenon of Terminal Velocity. Consider a falling raindrop. Initially, gravity accelerates it, causing its speed to increase. However, as it speeds up, the aerodynamic drag (fluid friction) acting upward also increases. Eventually, the upward drag (plus a tiny bit of buoyancy) exactly matches the downward pull of gravity. At this point, the net force becomes zero, acceleration stops, and the raindrop falls at a constant, safe speed Physical Geography by PMF IAS, Hydrological Cycle (Water Cycle), p.337. Without fluid friction, a raindrop falling from a cloud could potentially reach the speed of a bullet!

Concept	Description	Effect on Motion
Viscosity	Internal resistance within the fluid itself.	Determines how easily a fluid flows (e.g., molasses vs. water).
Fluid Friction (Drag)	Resistance exerted by a fluid on an object moving through it.	Opposes the motion of the object; increases with speed.
Terminal Velocity	The constant speed reached when drag equals gravitational pull.	The object stops accelerating and maintains a steady state.

Sources: Physical Geography by PMF IAS, Jet streams, p.384; Physical Geography by PMF IAS, Hydrological Cycle (Water Cycle), p.337

5. Air Resistance (Drag Force) (intermediate)

Imagine you are cycling on a calm day. As you pedal faster, you feel a stronger 'wind' pushing against your chest, even though there is no actual wind. This is Air Resistance (also known as Aerodynamic Drag). In physics, air is treated as a fluid. Just as it is harder to run through water than through air, any object moving through the atmosphere must push air molecules out of its way, creating a resistive force that acts in the opposite direction of motion. This is a crucial component of the frictional force that horizontal and vertical winds experience near the Earth's surface FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Atmospheric Circulation and Weather Systems, p.78.

The defining characteristic of air resistance is that it is velocity-dependent. Unlike the friction between two solid surfaces, which remains relatively constant, drag increases significantly as the object's speed increases. To understand this in a geographic context, consider a falling raindrop. Initially, the gravitational force pulls the drop downward, causing it to accelerate. As its velocity increases, the upward drag force also increases. Furthermore, because the raindrop is displaced in a fluid (air), a small buoyant force also pushes upward Science, Class VIII, Exploring Forces, p.76.

Eventually, a state of equilibrium is reached. The combined upward forces (Air Resistance + Buoyancy) become equal in magnitude to the downward force of Gravity. At this specific 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 steady, constant speed called Terminal Velocity. This is why raindrops do not strike the ground at supersonic speeds; the atmosphere acts as a natural brake Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306.

Force Phase	Condition	Effect on Motion
Initial Fall	Gravity > Drag	Object accelerates (speeds up)
Increasing Speed	Drag is rising	Acceleration decreases, but speed still rises
Terminal Velocity	Gravity = Drag + Buoyancy	Zero acceleration; Constant Speed

Sources: FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Atmospheric Circulation and Weather Systems, p.78; Science, Class VIII, Exploring Forces, p.76; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306

6. Terminal Velocity: The Equilibrium of Forces (exam-level)

Imagine a raindrop forming high in the clouds. If the Earth had no atmosphere, that tiny drop would accelerate continuously under gravity, hitting the ground at hundreds of kilometers per hour—effectively becoming a lethal projectile! Thankfully, fluid dynamics gives us Terminal Velocity, the speed at which the forces of nature reach a perfect "stalemate."

When an object starts falling, the primary force acting on it is Gravity (Weight), pulling it downward. However, as it moves through a fluid like air, it encounters Aerodynamic Drag (air resistance) and Buoyancy acting in the opposite direction. While the force of gravity remains constant, the drag force is "speed-dependent"—the faster the object falls, the harder the air pushes back against it. You can visualize this by sticking your hand out of a moving car window; the faster the car goes, the stronger the wind pushes your hand back.

As the falling object accelerates, the upward drag force grows until a critical moment occurs: the sum of the upward forces (Drag + Buoyancy) exactly equals the downward force of Gravity. At this point, the Net Force becomes Zero. According to Newton’s Second Law (F = ma), if the net force is zero, the acceleration must also be zero. The object doesn't stop moving; rather, it stops speeding up and continues to fall at a steady, constant speed called terminal velocity. This equilibrium is why raindrops of different sizes reach the ground at manageable speeds, as the air resistance eventually "fails to hold them" against gravity once they grow large enough to fall Physical Geography by PMF IAS, Hydrological Cycle (Water Cycle), p.337.

Phase of Fall	Force Relationship	Motion Status
Initial Release	Gravity > Drag	Accelerating Downward
Mid-Fall	Gravity > Drag (but Drag is increasing)	Still Accelerating (slower rate)
Terminal Velocity	Gravity = Drag + Buoyancy	Constant Velocity (Zero Acceleration)

Sources: Physical Geography by PMF IAS, Hydrological Cycle (Water Cycle), p.337

7. Solving the Original PYQ (exam-level)

This question perfectly bridges your understanding of Newtonian mechanics and fluid dynamics. When a raindrop begins its descent, it is initially governed by the downward pull of gravity. However, because air acts as a fluid medium, it exerts a resistive force known as viscous drag or air resistance. As you learned in the study of Stokes' Law, this resistive force is not constant; it increases as the velocity of the falling object increases. This dynamic interplay is the fundamental building block for understanding how objects behave within the Earth's atmosphere.

To arrive at the correct answer, you must visualize the force equilibrium. Initially, gravity is the dominant force, causing the raindrop to accelerate downward. As the drop speeds up, the upward aerodynamic drag grows stronger. Eventually, the magnitude of this drag (combined with a small amount of buoyancy) perfectly balances the downward force of gravity. At this precise moment, the net force acting on the raindrop becomes zero. Since there is no further acceleration, the drop continues to fall at a steady, maximum speed known as terminal velocity. This leads us directly to the correct choice: (C) its velocity goes on increasing for some time and then becomes constant.

UPSC often includes traps to test if you are applying physics in a vacuum or a real-world environment. Option (A) is a common pitfall; it assumes there is no air resistance, which is incorrect in our atmosphere. Option (B) contradicts the reality of gravitational pull, and Option (D) incorrectly suggests that the drop somehow "breaks" its steady state to speed up again without an external force. Mastering this concept of terminal velocity is essential for understanding precipitation patterns and the hydrological cycle, as highlighted in Physical Geography by PMF IAS.