Two identical blocks of ice, Aand B, float in water as shown in the figure given below. Which one among the following statements in this regard is correct?

1. Fundamentals of Mass, Weight, and Gravity (basic)

Welcome to your first step in mastering mechanics! To understand how the physical world works, we must first distinguish between two terms we often use interchangeably in daily life: mass and weight. While they might feel like the same thing when you're standing on a bathroom scale, in science, they represent two very different concepts.

Mass is defined as the quantity of matter present in an object or substance Science, Class VIII, NCERT (Revised ed 2025), Chapter 9, p.142. Think of it as the total count of atoms and molecules inside you. Because this count doesn't change regardless of where you go, your mass is constant. Whether you are on Earth, orbiting in a space station, or standing on the Moon, your mass remains exactly the same. We measure mass in units like grams (g) and kilograms (kg).

Weight, however, is a force. Specifically, it is the gravitational force with which a planet (like Earth) pulls an object toward its center Science, Class VIII, NCERT (Revised ed 2025), Chapter 5, p.75. Since weight is a force, its SI unit is the newton (N). Because gravity varies—for instance, the Moon’s pull is much weaker than Earth’s—your weight changes depending on your location, even though your mass stays the same Science, Class VIII, NCERT (Revised ed 2025), Chapter 5, p.72.

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Gravitational pull on an object.
Nature	Inherent and constant.	Variable (depends on gravity).
SI Unit	Kilogram (kg).	Newton (N).
Device	Two-pan balance.	Spring balance or digital scale.

An interesting point to note is that most scales we use (like digital balances) actually measure weight (the force pressing down), but they are calibrated to show you the result in kilograms. This works because the Earth's gravity is relatively uniform across the globe, allowing the device to "convert" the force it feels into the corresponding mass Science, Class VIII, NCERT (Revised ed 2025), Chapter 5, p.73.

Sources: Science, Class VIII, NCERT (Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.142; Science, Class VIII, NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.72-75

2. Understanding Density and Relative Density (basic)

At its simplest level, density tells us how 'compact' a substance is. Imagine two identical boxes: one filled with lead and the other with feathers. Even though they take up the same space, the lead box is much heavier because its particles are more closely packed Science, Class VIII NCERT, Particulate Nature of Matter, p.113. Mathematically, density (ρ) is defined as mass per unit volume (Density = Mass / Volume). In the International System of Units (SI), it is measured in kilograms per cubic meter (kg/m³).

While density is an absolute measure, Relative Density (also called Specific Gravity) is a comparison. It is the ratio of the density of a substance to the density of a reference material—usually pure water at 4 °C. Because it is a ratio of two similar quantities, relative density has no units. For example, the Earth’s overall density is 5.5, meaning it is 5.5 times as dense as water, while the Sun's density is approximately 1.41 times that of water Physical Geography by PMF IAS, The Solar System, p.23. If an object's relative density is less than 1, it will float in water; if it is greater than 1, it will sink.

Density is not a fixed number; it changes with temperature and pressure. Generally, as a substance gets hotter, its particles move faster and spread out, increasing volume and decreasing density. However, water is a fascinating exception. Water reaches its maximum density at 4 °C. When it cools further and turns into ice at 0 °C, it actually expands and becomes less dense, which is why ice floats on your refreshing summer drink rather than sinking to the bottom Science, Class VIII NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.148.

Feature	Density	Relative Density
Definition	Mass per unit volume of a substance.	Ratio of substance density to water density.
Units	kg/m³ or g/cm³	Unitless (Dimensionless)
Purpose	Measures absolute compactness.	Easy comparison to see if things sink or float.

Sources: Science, Class VIII NCERT, Particulate Nature of Matter, p.113; Physical Geography by PMF IAS, The Solar System, p.23; Science, Class VIII NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.148

3. Fluid Pressure and Pascal’s Law (intermediate)

In our journey through mechanics, we now move from the behavior of solid objects to the fascinating world of fluids (liquids and gases). Unlike solids, which exert pressure primarily in the direction of the applied force (usually downwards due to gravity), fluids are unique because their particles are free to move. This leads us to the fundamental definition of Pressure: it is the force acting per unit area (Pressure = Force / Area). In the international system (SI), we measure this in newtons per square metre (N/m²), a unit formally known as the pascal (Pa) Science, Class VIII . NCERT (Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.94.

One of the most vital principles to master is Pascal’s Law. It states that any pressure applied to a confined, incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container. Think of a water bottle with small holes at the same height: water spurts out with equal force from every side. This proves that liquids exert pressure not just at the bottom, but in all directions Science, Class VIII . NCERT (Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.85. This happens because the molecules in a liquid are constantly colliding with each other and the container walls, transferring momentum throughout the volume.

It is also important to distinguish how different states of matter respond to pressure. This comparison helps in understanding why hydraulic systems (like car brakes) use liquids rather than air:

Feature	Liquids	Gases
Compressibility	Nearly incompressible; volume barely changes under pressure.	Highly compressible; volume decreases significantly as pressure increases.
Density Change	Negligible change when pressure is applied.	Density increases as particles are forced closer together.

Science, Class VIII . NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.148

In practical UPSC terms, remember that this uniform transmission of pressure is what allows a small force applied to a small piston to lift a massive weight on a larger piston. Because the pressure (Force/Area) remains constant throughout the fluid, increasing the area on the output side multiplies the force!

Sources: Science, Class VIII . NCERT (Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.94; Science, Class VIII . NCERT (Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.85; Science, Class VIII . NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.148

4. Surface Tension and Capillary Action (intermediate)

Surface Tension is a fascinating property of liquids where the surface behaves like a stretched elastic membrane. At the molecular level, this occurs because molecules inside the liquid are pulled in all directions by their neighbors, resulting in a net force of zero. However, molecules at the surface have no liquid neighbors above them; they are pulled only sideways and inward. This creates an internal pressure that forces the liquid to occupy the least possible surface area, which is why raindrops naturally form spheres. While liquids have a definite volume and take the shape of their container Science, Class VIII, Particulate Nature of Matter, p.104, surface tension allows them to resist external forces, such as a needle floating on water or insects walking on a pond.

Capillary Action is the spontaneous flow of a liquid into a narrow tube or porous material. This movement isn't magic; it is driven by two competing forces: Cohesion (attraction between like molecules, like water-to-water) and Adhesion (attraction between unlike molecules, like water-to-glass). When the adhesive force between the liquid and the container wall is stronger than the cohesive force within the liquid, the liquid "climbs" the wall. This is a critical process in nature and agriculture. For instance, in arid regions, groundwater is pulled upward through tiny pores in the soil via capillary action. As the water reaches the surface and evaporates due to high temperatures, it leaves behind dissolved salts, creating hardpans or saline tracts known locally as kallar or reh Geography of India, Majid Husain, Agriculture, p.67.

Force Type	Definition	Role in Capillary Action
Adhesion	Attraction between liquid molecules and the surface.	Pulls the liquid upward along the surface of the tube/pore.
Cohesion	Attraction between the liquid molecules themselves.	Keeps the liquid column intact as it is pulled upward.

Sources: Science, Class VIII, Particulate Nature of Matter, p.104; Geography of India, Majid Husain, Agriculture, p.67; Fundamentals of Physical Geography, Class XI, Geomorphic Processes, p.45

5. Viscosity and Fluid Friction (intermediate)

Imagine pouring honey versus pouring water. The honey flows slowly and resists spreading; this internal resistance to flow is what we call viscosity. At a microscopic level, this happens because matter is composed of particles held together by interparticle forces of attraction. In liquids, these forces are strong enough to keep the particles close but weak enough to allow them to slide past one another Science, Class VIII, Particulate Nature of Matter, p.113. Viscosity is essentially "internal friction" between the layers of the fluid as they move at different velocities. When an object moves through a fluid, it encounters fluid friction (often called drag). This is an external resistive force that opposes the object's motion. The amount of drag depends on three main factors: the speed of the object, the shape of the object, and the nature of the fluid (its viscosity). To minimize this friction, nature and engineers use "streamlining"—shaping objects like birds, fish, and airplanes to cut through the fluid more efficiently. In the context of our planet, fluid friction plays a massive role in atmospheric circulation. Near the Earth's surface, friction between the air and the ground slows down the wind. However, as we move 2–3 km above the surface, the air becomes "free" from this surface frictional effect Physical Geography by PMF IAS, Jet streams, p.384. Without this friction to slow them down, upper-atmospheric winds can reach much higher velocities, eventually resulting in phenomena like geostrophic winds where the pressure gradient is balanced solely by the Coriolis force FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI, Atmospheric Circulation and Weather Systems, p.79.

Feature	Viscosity	Fluid Friction (Drag)
Definition	Internal resistance of a fluid to flow.	Resistive force exerted by a fluid on an object moving through it.
Cause	Interparticle attractions between fluid layers.	Collision of fluid particles with the surface of a moving object.
Example	Honey is more viscous than water.	Air resistance acting on a falling skydiver.

Sources: Science, Class VIII (NCERT 2025), Particulate Nature of Matter, p.113; Physical Geography by PMF IAS, Jet streams, p.384; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025), Atmospheric Circulation and Weather Systems, p.79

6. Archimedes’ Principle and Buoyant Force (exam-level)

Imagine pushing an empty plastic bottle into a bucket of water. You will feel a distinct, stubborn resistance pushing back against your hand. This upward push is what we call buoyant force or upthrust (Science, Class VIII, Chapter 5, p.76). This phenomenon is universal; whether it is a massive ship in the ocean or a tiny ice cube in a glass, every liquid exerts this upward force on objects immersed in it. The strength of this force is defined by Archimedes’ Principle, which states that the upward buoyant force is exactly equal to the weight of the fluid displaced by the object.

For an object to float successfully, it must achieve static equilibrium. In simple terms, the downward force (the object's weight) must be perfectly balanced by the upward force (the buoyant force). As noted in Science, Class VIII, Chapter 5, p.76, if the weight of the displaced liquid is less than the weight of the object, the object will sink. If they are equal, the object floats. This leads to a powerful deduction: if two different objects have the same mass and both are floating, they must be experiencing the same buoyant force to remain balanced. Therefore, they must both displace an identical volume of water to generate that specific force.

Crucially, the orientation of the object—whether it is floating vertically like a buoy or horizontally like a log—does not change the volume of water it must displace to stay afloat. As long as the mass remains constant, the "footprint" of the submerged portion (the total volume below the waterline) will remain the same because the water is only reacting to the weight it needs to support (Science, Class VIII, Chapter 5, p.77).

Condition	Result	Reasoning
Weight > Buoyant Force	Sinks	Downward gravity overpowers the liquid's upthrust.
Weight = Buoyant Force	Floats	The forces are in equilibrium; the object is supported.

Sources: Science, Class VIII. NCERT (2025), Exploring Forces, p.76; Science, Class VIII. NCERT (2025), Exploring Forces, p.77

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

When we place an object in water, two opposing forces immediately come into play: the gravitational force pulling it downward and an upward push from the water known as the buoyant force. Have you ever noticed how a mug feels lighter when it is submerged in a bucket of water? This is because the upward buoyant force is supporting some of its weight Science, Class VIII NCERT, Exploring Forces, p.76. For an object to float in static equilibrium, these two forces must be perfectly balanced. If the gravitational pull (weight) is greater than the maximum possible buoyant force, the object sinks.

The Law of Flotation is a specific application of Archimedes' Principle. It states that a floating object displaces a weight of fluid exactly equal to its own weight. This leads to a fascinating realization: if you have two identical wooden blocks with the same mass, they must experience the same buoyant force to stay afloat. Because the buoyant force depends entirely on the weight of the water displaced, both blocks must displace the exact same volume of water Science, Class VIII NCERT, Exploring Forces, p.79.

Crucially, the orientation of the object does not change this balance. Whether a block floats horizontally (lying flat) or vertically (standing tall), as long as its mass remains the same, the volume of the submerged portion remains identical. While the depth of the submerged end might change based on the block's shape, the total amount of water "pushed aside" to create that upward force remains constant to satisfy the equilibrium condition.

Condition	Result	Force Relation
Weight > Max Buoyant Force	Object Sinks	W > B
Weight = Buoyant Force	Object Floats (Equilibrium)	W = B
Density < Fluid Density	Object Floats partially submerged	ρ_obj < ρ_fluid

Sources: Science, Class VIII NCERT, Exploring Forces, p.76; Science, Class VIII NCERT, Exploring Forces, p.79

8. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamental mechanics of Archimedes' Principle and the Law of Flotation, this question serves as the perfect test of your conceptual clarity. The key to solving this lies in recognizing that for any object in static equilibrium while floating, the upward buoyant force must exactly balance the downward force of gravity (the object's weight). Because the blocks are described as identical, they possess the same mass and weight. According to Science, Class VIII NCERT, the buoyant force is equal to the weight of the fluid displaced; therefore, to support the same weight, both blocks must displace an equal weight—and consequently an equal volume—of water.

To arrive at (D) The two blocks displace equal volumes of water since they have the same specific gravity and same mass, you must look past the visual orientation of the blocks. Whether a block is submerged vertically or horizontally, the total volume of water it needs to push aside to generate enough upward force to stay afloat remains constant. This is a classic application of the principle of buoyancy where the specific gravity (the ratio of the density of the object to the fluid) determines the fraction of the volume that stays submerged, regardless of the shape's orientation.

UPSC frequently uses "geometrical traps" like those found in options (A), (B), and (C) to distract you with secondary physics concepts. While it is true that hydrostatic pressure increases with depth (as hinted in B) and surface area affects force distribution (as hinted in A and C), these factors do not change the net displacement required for flotation. These options are designed to trick students who overthink the local pressure rather than focusing on the global equilibrium of the system. Always remember: if the mass and the fluid are the same, the volume displaced must be the same to maintain equilibrium.