Consider the following statements : I. If temperature rises, the coefficient of viscosity of a liquid decreases. II. The velocity of a falling raindrop attains a constant value because of viscous force exerted by air. Which of these is/are correct?

1. Introduction to Fluids: Cohesive and Adhesive Forces (basic)

Welcome to your first step in mastering Thermal Physics! To understand how heat affects matter, we must first understand the "invisible glue" that holds everything together. Matter is composed of tiny particles that are constantly in a tug-of-war between thermal energy (which makes them move) and interparticle forces of attraction (which make them stick together). As noted in Science, Class VIII. NCERT (Revised ed 2025), Particulate Nature of Matter, p.112, the state of matter—whether it is a solid, liquid, or gas—is determined by which of these two wins the battle.

In the study of fluids, we categorize these attractive forces into two critical types:

• Cohesive Forces: These are the attractive forces between identical molecules. Think of this as "self-love" or internal sticking. For example, cohesive forces are what cause water molecules to cling to each other to form a spherical droplet. In solids, these forces are incredibly strong, keeping particles in fixed positions; in liquids, they are strong enough to keep a definite volume but weak enough to allow particles to slide past one another (Science, Class VIII. NCERT (Revised ed 2025), Particulate Nature of Matter, p.113).
• Adhesive Forces: These are the attractive forces between different types of molecules. This is why water "wets" a glass surface or why a liquid level might slightly drop when poured from a dirty container because some molecules stick to the walls (Science, Class VIII. NCERT (Revised ed 2025), Particulate Nature of Matter, p.104).

The balance between these forces defines how a fluid behaves. For instance, when you heat a substance, you are adding thermal energy. At the melting point, this energy becomes sufficient to overcome the strong cohesive forces of a solid, allowing the particles to move more freely as a liquid (Science, Class VIII. NCERT (Revised ed 2025), Particulate Nature of Matter, p.112). Understanding this "stickiness" is the foundation for everything from how raindrops fall to how industrial lubricants work.

Force Type	Attraction Between...	Common Example
Cohesion	Same substance molecules	Mercury forming beads on a table.
Adhesion	Different substance molecules	Glue sticking to paper or water wetting a cloth.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Particulate Nature of Matter, p.104, 112, 113

2. Fluids at Rest: Pressure and Buoyancy (basic)

To understand fluids at rest, we must first look at Pressure. Pressure is defined as the force acting perpendicularly on a unit area of a surface (Pressure = Force / Area). In the SI system, we measure force in Newtons (N) and area in square metres (m²), making the unit of pressure N/m², also known as the Pascal (Pa) Science, Class VIII, NCERT (Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.82. Unlike solids, which mainly exert pressure downwards due to gravity, fluids (liquids and gases) exert pressure in all directions—downwards, sideways, and even upwards against the walls of their container.

This upward pressure leads us to the concept of Buoyancy. Have you ever noticed how a plastic bottle snaps back to the surface when you try to push it under water? This is because fluids exert an upward force on any object immersed in them, known as Upthrust or the buoyant force. The magnitude of this force was famously quantified by the Greek scientist Archimedes. Archimedes’ Principle states that when an object is fully or partially immersed in a fluid, it experiences an upward force equal to the weight of the fluid it displaces Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.76.

Whether an object sinks or floats depends on the "tug-of-war" between its own weight (pulling it down) and the buoyant force (pushing it up). We can summarize the logic of flotation as follows:

Scenario	Force Comparison	Outcome
Weight of object > Weight of displaced liquid	Downward force wins	The object sinks
Weight of object = Weight of displaced liquid	Forces are balanced	The object floats (equilibrium)
Weight of object < Weight of displaced liquid	Upward force wins	The object rises to the surface

Sources: Science, Class VIII, NCERT (Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.82; Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.76

3. Streamline vs. Turbulent Flow (intermediate)

To understand how fluids move, we must first look at the orderliness of their motion. Imagine a calm, steady stream where every drop of water follows the exact path of the one before it. This is known as Streamline (or Laminar) Flow. In this state, the velocity of every passing particle at any fixed point remains constant over time. This steady movement is often driven by a pressure difference between two points, much like how water flows through a tube only when one end is at a higher pressure or elevation Science, class X (NCERT 2025 ed.), Electricity, p.173. In streamline flow, layers of fluid slide smoothly over one another without mixing significantly. As the velocity of the fluid increases, it eventually hits a threshold called the critical velocity. Beyond this point, the smooth order collapses into Turbulent Flow. In turbulence, the motion becomes chaotic; particles move in zig-zags, forming small whirlpools known as eddies. We see this transition in nature when a river loses its straight course and begins to work laterally on its banks, creating complex patterns like meanders due to irregularities in the terrain and changes in flow speed FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Landforms and their Evolution, p.51. One of the most important consequences of fluid flow is the relationship between speed and pressure, described by Bernoulli's Principle. It states that within a horizontal flow, points where the fluid speed is higher will actually experience less pressure than points where the fluid is moving slower Physical Geography by PMF IAS, Tropical Cyclones, p.358. This principle explains everything from how airplanes fly to how tropical cyclones behave.

Feature	Streamline (Laminar) Flow	Turbulent Flow
Path of Particles	Orderly, following the preceding particle.	Chaotic, irregular, and zig-zag.
Velocity	Below critical velocity; constant at a point.	Above critical velocity; fluctuates rapidly.
Energy Loss	Minimal; governed by internal friction (viscosity).	High; significant energy dissipated in eddies.

Sources: Science, class X (NCERT 2025 ed.), Electricity, p.173; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Landforms and their Evolution, p.51; Physical Geography by PMF IAS, Tropical Cyclones, p.358

4. Surface Tension and Capillarity (intermediate)

At the molecular level, Surface Tension is the result of an imbalance of forces. Imagine a molecule inside a glass of water; it is pulled equally in all directions by its neighbors. However, a molecule at the surface has no liquid neighbors above it, creating a net inward pull. This causes the surface to behave like a stretched elastic membrane, always trying to minimize its surface area. This is why small raindrops are spherical—the sphere is the shape with the least surface area for a given volume. While surface tension is about molecules sticking to each other (cohesion), Capillarity involves the interaction between liquid molecules and a solid surface (adhesion). When you place a very thin tube into water, the adhesive force between the water and the glass is stronger than the water's internal cohesion. This causes the water to 'climb' the walls of the tube. This phenomenon is critical in nature; for instance, while capillaries in the human body are biological vessels for blood exchange as noted in Science, Class X, Life Processes, p.93, the physical principle of capillary action is what allows water to move up through the narrow vessels of a giant tree against gravity. In the context of thermal physics, temperature plays a decisive role. As the temperature of a liquid increases, the molecules gain kinetic energy and vibrate more vigorously. This increased motion weakens the intermolecular cohesive forces that hold the surface together. Consequently, surface tension decreases as temperature rises. This is why hot water is better for cleaning clothes; the lower surface tension allows the water to penetrate smaller pores and fibers more effectively.

Force Type	Interaction	Resulting Phenomenon
Cohesion	Between similar molecules	Surface Tension / Droplet formation
Adhesion	Between different molecules	Capillary rise / Wetting of surfaces

Sources: Science, Class X, Life Processes, p.93; Science, Class VIII, Exploring Forces, p.76

5. Bernoulli's Principle and its Applications (exam-level)

At its heart, Bernoulli’s Principle is an expression of the Law of Conservation of Energy applied to flowing fluids (liquids and gases). It tells us a seemingly counterintuitive truth: as the speed of a moving fluid increases, the pressure within that fluid decreases. Imagine a fluid traveling through a pipe that narrows; to maintain a steady flow, the fluid must speed up in the narrow section. Bernoulli’s Principle explains that the energy required for this acceleration comes at the expense of the fluid's internal pressure.

This principle is mathematically represented as the sum of pressure energy, kinetic energy (motion), and potential energy (height) remaining constant along a streamline. In a horizontal flow where height doesn't change, the relationship is a simple trade-off between velocity and pressure. This has profound real-world implications, particularly in how wind interacts with surfaces. For instance, higher wind speeds decrease air pressure, which directly influences the rate of evaporation by lowering the atmospheric resistance against water molecules trying to escape into the air Physical Geography by PMF IAS, Tropical Cyclones, p.358.

We see Bernoulli’s Principle in action across various phenomena:

• Aerodynamics: The curved shape of an airplane wing (aerofoil) forces air to move faster over the top surface than the bottom, creating lower pressure above and generating lift.
• The Magnus Effect: A spinning ball curves in flight because the spin accelerates air on one side (lower pressure) and slows it on the other (higher pressure).
• Atomizers and Sprayers: When you squeeze the bulb of a perfume sprayer, fast-moving air passes over the top of a tube, creating a low-pressure zone that sucks the liquid upward.

Feature	High Fluid Speed Zone	Low Fluid Speed Zone
Internal Pressure	Lower	Higher
Kinetic Energy	Higher	Lower
Example	Air over a curved wing	Air under a flat wing

Sources: Physical Geography by PMF IAS, Tropical Cyclones, p.358

6. Viscosity: Internal Friction in Fluids (intermediate)

In our study of thermal physics, we must understand Viscosity, which is essentially the "internal friction" of a fluid. Imagine a fluid as a series of thin layers sliding over one another. Viscosity is the measure of resistance that one layer offers to the adjacent layer moving past it. Just as solid surfaces experience friction, fluid layers experience viscous drag. This property determines how "thick" or "runny" a fluid is—for instance, honey has a much higher viscosity than water.

The behavior of viscosity changes dramatically with temperature, and the logic differs between liquids and gases:

• In Liquids: The primary cause of viscosity is the cohesive forces between molecules. When the temperature rises, the molecules gain thermal energy, allowing them to overcome these attractive forces more easily. Consequently, the "stickiness" decreases, and the viscosity of a liquid decreases as temperature increases.
• In Gases: Cohesive forces are negligible. Here, viscosity arises from the random collisions of molecules between layers. As temperature increases, gas molecules move faster and collide more frequently. These increased collisions act like "traffic jams," creating more resistance to flow. Thus, the viscosity of a gas increases with temperature.

A fascinating application of this concept is Terminal Velocity. When an object, like a raindrop, falls through a fluid (air), it is acted upon by three main forces: the downward force of weight, and two upward forces—the buoyant force (or upthrust) Science, Class VIII, Exploring Forces, p.77 and the viscous drag. Initially, the object accelerates due to gravity. However, as its speed increases, the viscous drag (governed by Stokes' Law) also increases. Eventually, the sum of the upward forces perfectly balances the downward weight. At this point, the net force becomes zero Science, Class VIII, Exploring Forces, p.65, and the object stops accelerating, continuing at a constant speed known as terminal velocity.

Fluid Type	Temp Increase Effect	Underlying Reason
Liquids	Viscosity Decreases	Weakening of cohesive molecular bonds.
Gases	Viscosity Increases	Increased frequency of molecular collisions.

Sources: Science, Class VIII (NCERT Revised ed 2025), Exploring Forces, p.77; Science, Class VIII (NCERT Revised ed 2025), Exploring Forces, p.65

7. Temperature Dependency of Viscosity (exam-level)

To understand why fluids behave differently under heat, we must look at viscosity—the internal resistance a fluid offers to flow. Think of it as 'fluid friction.' The way temperature affects this resistance depends entirely on whether we are dealing with a liquid or a gas, as their molecular structures are fundamentally different. In liquids, viscosity is primarily governed by cohesive forces—the 'stickiness' between molecules. When you heat a liquid, the particles gain kinetic energy and move more vigorously. As noted in the study of matter, rising temperatures cause particles to move apart, resulting in a decrease in the interparticle forces of attraction Science, Class VIII, Particulate Nature of Matter, p.105. Consequently, the liquid becomes thinner and flows more easily; for example, hot honey is much less viscous than cold honey. Conversely, the viscosity of gases increases with temperature. This seems counter-intuitive, but in gases, viscosity is not about cohesive forces (which are negligible) but about molecular collisions. As temperature rises, gas molecules move faster and collide more frequently. These chaotic collisions interfere with the organized flow of the gas, creating more internal resistance. In the context of atmospheric science, this means air actually provides more viscous resistance when it is warmer. This resistance plays a crucial role in phenomena like terminal velocity; for instance, a falling raindrop eventually stops accelerating because the upward viscous drag of the air balances the downward force of gravity, leading to a constant speed.

Fluid Type	Effect of Temperature Increase	Primary Reason
Liquids	Viscosity Decreases	Thermal energy overcomes cohesive forces; particles move apart.
Gases	Viscosity Increases	Increased molecular collisions and momentum transfer.

Sources: Science, Class VIII, Particulate Nature of Matter, p.105

8. Stokes' Law and Terminal Velocity (exam-level)

Have you ever wondered why a raindrop, falling from thousands of meters in the sky, doesn't hit the ground with the speed of a bullet? According to the simple laws of gravity, it should accelerate indefinitely. The reason it doesn't is fluid friction or viscous drag. Just as solid surfaces offer friction, fluids (liquids and gases) exert a resistive force on objects moving through them Science Class VIII, Exploring Forces, p.68. For a small spherical object like a raindrop, this resistance is governed by Stokes' Law, which states that the viscous force (F) is directly proportional to the radius of the sphere (r), its velocity (v), and the coefficient of viscosity (η) of the fluid: F = 6πηrv.

When an object starts falling through a fluid, it initially accelerates due to gravity. however, as its velocity increases, the upward viscous drag also increases. Eventually, a point is reached where the downward force (weight) is perfectly balanced by the sum of upward forces: the buoyant force and the viscous drag. At this equilibrium, the net force becomes zero, acceleration stops, and the object continues to fall at a constant speed called Terminal Velocity. This is why raindrops reach a steady speed rather than accelerating dangerously Physical Geography, Hydrological Cycle, p.337. It is a delicate balance of forces, much like how the vertical pressure gradient in our atmosphere is generally balanced by gravity to prevent strong upward winds Physical Geography, Pressure Systems and Wind System, p.306.

In the context of thermal physics, it is critical to understand how temperature influences this process. The viscosity (η) of a fluid is not constant; it changes with heat. In liquids, rising temperatures provide thermal energy that helps molecules overcome the cohesive forces holding them together, causing viscosity to decrease. Conversely, in gases, increasing the temperature increases the random motion and collisions of molecules, which actually increases viscosity. Therefore, a sphere will reach a higher terminal velocity in a warmer liquid (because the fluid is "thinner") but a lower terminal velocity in a warmer gas (because the gas becomes "thicker" or more resistant).

Sources: Science Class VIII, Exploring Forces, p.68; Physical Geography by PMF IAS, Hydrological Cycle (Water Cycle), p.337; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306

9. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamental mechanics of fluids, this question serves as a perfect synthesis of intermolecular forces and kinematics. Statement I tests your understanding of the molecular kinetic theory, where you learned that in liquids, viscosity is primarily a result of cohesive forces between molecules. As temperature increases, the thermal energy overcomes these bonds, allowing the fluid to flow more easily. Conversely, Statement II applies Stokes' Law and the principle of equilibrium. You have studied how a body moving through a fluid experiences a resistive force; here, the air acts as that fluid medium, providing the viscous drag necessary to counter the acceleration of gravity.

To arrive at the correct answer, (C) Both I and II, your reasoning should follow a two-step verification. First, recall the distinct behavior of different states of matter: while gases become more viscous with heat due to increased molecular momentum transfer, liquids always experience a decrease—making Statement I a solid factual check. Second, visualize the forces on a falling raindrop: Gravity pulls it down, while viscous force (air resistance) acts upward. When these opposing forces balance, the net force becomes zero, leading to terminal velocity. This integration of thermal and mechanical properties is a hallmark of the concepts found in NCERT Physics Class XI.

UPSC often sets traps by presenting statements that are individually plausible but require distinct conceptual applications. Options (A) and (B) are common pitfalls for students who might confuse liquid viscosity with gas viscosity or those who fail to recognize air as a fluid that exerts its own viscous drag. A common mistake is to assume "viscosity" only applies to thick liquids like honey, forgetting that gases (air) are also fluids that exert resistance. By confirming both the thermal dependence and the mechanical equilibrium, you avoid the trap of "half-knowledge" that often leads candidates to choose only one correct statement.