Assertion (A) : An iron ball floats on mercury but gets immersed in water. Reason (R) : The specific gravity of iron is more than that of mercury.

1. Understanding Density and Mass-Volume Relationships (basic)

To understand why things behave differently in water or other fluids, we must first look at the fundamental relationship between mass and volume. Every piece of matter possesses mass (the amount of matter in it) and occupies a certain amount of space, which we call volume Science, Class VIII, Chapter 9, p.140. Density is simply the measure of how much mass is packed into a unit of that volume. You can think of it as the "compactness" of a substance.

Mathematically, we express this as: Density = Mass / Volume. Because density is a ratio of mass to volume, its SI unit is kilogram per cubic metre (kg/m³). However, in a laboratory or daily life, we often use smaller units like grams per cubic centimetre (g/cm³) or grams per millilitre (g/mL) Science, Class VIII, Chapter 9, p.141. An important characteristic of density is that it is independent of the shape or size of the object. Whether you have a tiny iron nail or a massive iron girder, the density of iron remains the same at a constant temperature and pressure.

When we want to compare substances easily, we use a concept called Relative Density (also known as specific gravity). This is a unitless number calculated by dividing the density of a substance by the density of water at the same temperature Science, Class VIII, Chapter 9, p.141. If a substance has a relative density greater than 1, it is denser than water; if it is less than 1, it is less dense than water.

This comparison is the secret to flotation. When an object is placed in a fluid, whether it sinks or floats depends entirely on the relative densities of the object and the fluid. An object will float if its density is lower than the fluid it is placed in, and it will sink if its density is higher. This explains why a heavy log of wood floats on water while a tiny grain of sand sinks—it isn't about total weight, but about how that weight is distributed across its volume.

Sources: Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.140; Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.141

2. Relative Density and Specific Gravity (basic)

Welcome to the second step of our journey! To understand why some objects sink while others float, we must look beyond simple weight and explore Relative Density (often called Specific Gravity). At its core, density is the mass of a substance per unit volume. However, in science and geography, we often find it more useful to compare a substance's density to a standard reference—usually pure water.

Relative Density is defined as the ratio of the density of a substance to the density of water at a specific temperature. Mathematically, it is expressed as:
Relative Density = Density of substance / Density of water
Because this is a ratio of two identical units (e.g., kg/m³ divided by kg/m³), the units cancel out. Therefore, Relative Density is a dimensionless number—it has no units Science, Class VIII . NCERT(Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.141.

This concept is the "master key" to predicting buoyancy. If an object's relative density is greater than 1, it is denser than water and will sink. If it is less than 1, it will float. For instance, oil floats on water because its density is lower than that of water Science, Class VIII . NCERT(Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.150. In a broader context, the Earth's overall density is 5.5 times that of water (Relative Density = 5.5), whereas the Sun’s density is only 1.41 times that of water Physical Geography by PMF IAS, The Solar System, p.23.

It is important to remember that flotation is always relative to the fluid. Consider an iron ball: its density is roughly 7.9 g/cm³. Since water's density is 1 g/cm³, the iron ball sinks in water. However, Mercury is a liquid with a much higher density (about 13.6 g/cm³). Because iron is less dense than mercury, the iron ball will actually float on a pool of mercury! This principle also drives our planet's systems; for example, in the oceans, colder and saltier water is denser, causing it to sink and create deep-sea currents Physical Geography by PMF IAS, Ocean Movements Ocean Currents And Tides, p.487.

Sources: Science, Class VIII . NCERT(Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.141, 150; Physical Geography by PMF IAS, The Solar System, p.23; Physical Geography by PMF IAS, Ocean Movements Ocean Currents And Tides, p.487

3. Archimedes' Principle and Buoyancy (intermediate)

Have you ever noticed how you feel lighter while swimming, or how a heavy piece of wood effortlessly stays atop a lake while a tiny pebble sinks? This phenomenon is governed by buoyancy. When any object is placed in a fluid (liquid or gas), the fluid exerts an upward force on it. This upward force is known as upthrust or the buoyant force Science, Class VIII . NCERT, Exploring Forces, p.77. It is measured in Newtons (N), just like any other force.

The magnitude of this force was first 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, Exploring Forces, p.76. Think of it as a trade-off: to enter the water, the object must push aside some volume of liquid; in return, that liquid pushes back with a force equal to its own weight. This principle is so fundamental that it even explains large-scale geological movements, such as the buoyancy forces that contribute to the movement of tectonic plates Physical Geography by PMF IAS, Tectonics, p.95.

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

Scenario	Force Comparison	Result
Object Sinks	Weight of object > Weight of displaced liquid	The downward pull of gravity wins.
Object Floats	Weight of object = Weight of displaced liquid	The forces are balanced.

This explains why materials with different densities behave differently. For instance, an iron ball (density ≈ 7.9 g/cm³) will sink in water because it cannot displace enough water weight to match its own weight. However, that same iron ball will float in mercury because mercury is incredibly dense (specific gravity ≈ 13.6). Because mercury is so heavy, the iron ball only needs to displace a small volume of it to balance its own weight, allowing it to stay afloat Science, Class VIII . NCERT, Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.151.

Sources: Science, Class VIII . NCERT (Revised ed 2025), Exploring Forces, p.76-77; Physical Geography by PMF IAS, Tectonics, p.95; Science, Class VIII . NCERT (Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.151

4. Fluid Pressure and Pascal's Law (intermediate)

In our journey through mechanics, we must understand that fluids (both liquids and gases) behave differently than solids. While a solid block exerts pressure only on the surface it rests upon, a fluid exerts pressure in all directions. This is because the molecules in a fluid are in constant motion, colliding with every surface they touch. As noted in Science, Class VIII . NCERT(Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.85, liquids exert pressure not only at the bottom of a container but also on its sides. This is why water spurts out horizontally from a hole in a bucket or a leaking pipe.

This brings us to a fundamental principle known as Pascal’s Law. It states that any pressure applied to an enclosed, incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of the container. Imagine a hydraulic jack: you apply a small force on a small piston, and that pressure travels through the oil to a larger piston. Because the pressure (Force/Area) remains constant, the larger area of the second piston results in a much greater lifting force. This makes fluids incredible force multipliers in engineering.

Finally, we must consider why objects behave differently when placed in these fluids. This is governed by relative density (or specific gravity). An object will float if its density is less than the density of the fluid it is in, and sink if it is denser. This happens because the fluid exerts an upward force (buoyancy) equal to the weight of the fluid displaced. If an object is very dense—like iron—it cannot displace enough water to match its own weight, so it sinks. however, if that same iron is placed in a much denser liquid like mercury, the upward buoyant force is much stronger, allowing the iron to float. Understanding this relationship between pressure, density, and buoyancy is key to mastering fluid mechanics.

Sources: Science, Class VIII . NCERT(Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.84-85

5. Surface Tension and Capillarity (intermediate)

Imagine the surface of a liquid as a stretched elastic membrane. This phenomenon is known as Surface Tension. It arises because molecules within a liquid are attracted equally in all directions by neighboring molecules, but those at the surface lack neighbors above them. This creates a net inward pull, causing the liquid surface to contract and behave like a 'skin.' This is why raindrops form spheres (the shape with the minimum surface area) and why certain insects can walk on water without sinking. While buoyancy (or upthrust) is the upward force exerted by a fluid that depends on the volume of liquid displaced Science, Class VIII (NCERT 2025), Chapter 5: Exploring Forces, p.76, surface tension is a different force altogether. It can support the weight of a small, dense object (like a greased needle) even if that object would normally sink based on its density. However, once the surface 'skin' is broken, the laws of buoyancy and density take over completely. When we look at very narrow spaces, we encounter Capillarity. This is the ability of a liquid to flow in narrow spaces without the assistance of, or even in opposition to, external forces like gravity. This happens because of two competing forces: adhesion (attraction between the liquid and the container wall) and cohesion (attraction between liquid molecules). If adhesion is stronger than cohesion, the liquid 'climbs' the walls. A classic example is the movement of water and minerals through the thin xylem tubes in plants, allowing life-sustaining fluids to reach the highest leaves Science-Class VII (NCERT 2025), Chapter 10: Life Processes in Plants, p.148.

Concept	Primary Cause	Real-world Example
Surface Tension	Inward Cohesive forces	Spherical shape of water droplets
Capillarity	Adhesion > Cohesion	Water rising in a cotton wick or plant stem

Sources: Science, Class VIII (NCERT 2025), Chapter 5: Exploring Forces, p.76; Science-Class VII (NCERT 2025), Chapter 10: Life Processes in Plants, p.148

6. Viscosity and Fluid Dynamics (exam-level)

To master fluid dynamics, we must first understand the equilibrium between solids and fluids. This behavior is governed by Archimedes’ Principle, which states that any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. As we see in Science, Class VIII, NCERT (2025), Chapter 9, p. 150, this principle allows us to measure a solid's volume through the displacement of water. However, whether that object actually sinks or floats depends on the interplay between the object's weight and this buoyant force. At the heart of this interaction is Density (mass per unit volume) and Specific Gravity (the ratio of a substance's density to the density of water). If an object is denser than the fluid, it cannot displace enough fluid weight to match its own weight before it is fully submerged, causing it to sink. Conversely, if the fluid is denser than the object, the object will float. For example, consider the relationship between Iron, Water, and Mercury:

Substance	Approx. Density (g/cm³)	Relative to Water	Behavior in Mercury
Water	1.0	Reference (1.0)	Floats (less dense)
Iron	7.9	Heavier (7.9)	Floats
Mercury	13.6	Much Heavier (13.6)	N/A (The Fluid)

As shown in Science, Class VIII, NCERT (2025), Chapter 9, p. 141, understanding density conversion is vital. Because Iron (7.9 g/cm³) is denser than water (1.0 g/cm³), it sinks in your glass of water. However, Mercury is exceptionally dense (13.6 g/cm³). Since Iron's density is significantly lower than Mercury's, an iron ball will displace a weight of mercury equal to its own weight while only being partially submerged, allowing it to float effortlessly on the liquid metal's surface.

Sources: Science, Class VIII, NCERT (2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.150-151; Science, Class VIII, NCERT (2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.141

7. The Law of Flotation and Comparative Densities (exam-level)

When we observe objects in a liquid, our intuition often tells us that "heavy" things sink and "light" things float. However, physics teaches us that flotation is not determined by weight alone, but by density—the amount of mass packed into a specific volume. An object floats when the upward buoyant force (or upthrust) exerted by the liquid is equal to the downward force of gravity acting on the object. This is rooted in Archimedes' Principle, which states that any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.76

To understand why a material like iron behaves differently in water versus mercury, we must look at Comparative Density (often expressed as Specific Gravity). An object will sink if its density is greater than the density of the liquid, because it cannot displace enough liquid to match its own weight. Conversely, if the liquid is denser than the object, the object will float. As noted in your studies, while washing rice, the lighter husk floats because its density is lower than water, while the denser rice grains sink. Science, Class VIII. NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.140

Substance	Approx. Density (g/cm³)	Behavior in Water (1.0 g/cm³)	Behavior in Mercury (13.6 g/cm³)
Water	1.0	-	Floats
Iron	7.9	Sinks	Floats
Mercury	13.6	Sinks	-

In the case of an iron ball, it sinks in water because iron (7.9 g/cm³) is much denser than water (1.0 g/cm³). However, mercury is an incredibly dense liquid (13.6 g/cm³). Because mercury is nearly twice as dense as iron, the iron ball only needs to displace a small volume of mercury to equal its total weight. Therefore, the iron ball floats on the surface of mercury, much like a piece of wood floats on water.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.76; Science, Class VIII. NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.140

8. Solving the Original PYQ (exam-level)

Now that you have mastered the concepts of density and buoyancy, this question serves as the perfect application of how physical properties dictate behavior in fluids. To solve this, you must synthesize Archimedes’ Principle with the relative specific gravities of materials. Recall that an object floats only if it is less dense than the fluid it displaces. As explained in Science, Class VIII, NCERT (Revised ed 2025), the relationship between the density of the solute and the solvent determines whether an object will remain buoyant or submerge.

Let’s walk through the logic like a seasoned aspirant. First, evaluate the Assertion (A): we know iron (density ≈7.9 g/cm³) is less dense than mercury (density ≈13.6 g/cm³), meaning it must float. Simultaneously, iron is denser than water (density ≈1 g/cm³), which explains why it sinks. Thus, Assertion (A) is factually true. Next, examine Reason (R). It claims iron has a higher specific gravity than mercury. From our data, we know this is mathematically impossible; if iron were denser, it would sink in mercury. Since the Reason itself is a false statement, the entire causal link is broken. Therefore, the correct answer is (C).

UPSC often uses Assertion-Reasoning questions as a trap for students who rush. The most common pitfall is selecting (A) or (B) simply because the Assertion "sounds right" and the Reason uses scientific terminology. However, if any part of a statement is factually incorrect—as is the case with the specific gravity comparison in (R)—options (A) and (B) are immediately eliminated. Always verify the individual truth of both statements independently before attempting to find a logical connection between them.