For a steel boat floating on a lake, the weight of the water displaced by the boat is

1. Density and Relative Density (basic)

At the heart of mechanics lies the understanding of how matter occupies space. Density is defined as the mass present in a unit volume of a substance. Mathematically, we express this as Density = Mass / Volume Science, Class VIII. NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.140. It is an intrinsic property of a material, meaning a single drop of oil has the same density as a whole barrel of the same oil. However, density is not fixed forever; it changes with temperature and pressure. For instance, as water gets colder or more saline, it becomes denser and tends to sink, which is a fundamental driver of ocean currents Physical Geography by PMF IAS, Ocean Movements Ocean Currents And Tides, p.487.

To make density easier to work with, we often compare it to a standard reference—usually pure water. This comparison is known as Relative Density (or Specific Gravity). It is the ratio of the density of a substance to the density of water at a specific temperature Science, Class VIII. NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.150. Since it is a ratio of two similar quantities, the units cancel out, leaving Relative Density as a pure number without units. For example, if aluminum has a density of 2.7 g/cm³ and water is roughly 1.0 g/cm³, the relative density of aluminum is 2.7, indicating it is 2.7 times denser than water Science, Class VIII. NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.141.

Feature	Density	Relative Density
Definition	Mass per unit volume.	Ratio of substance density to water density.
Units	g/cm³ or kg/m³.	None (Dimensionless).
Dependency	Changes with temp/pressure.	Comparison at a specific temperature.

Sources: Science, Class VIII. NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.140-141, 150; Physical Geography by PMF IAS, Ocean Movements Ocean Currents And Tides, p.487

2. Understanding Fluid Pressure and Upthrust (basic)

To understand why things float or sink, we must first look at how fluids (liquids and gases) behave under the influence of gravity. Unlike a solid block that primarily exerts pressure downwards on a surface, a fluid exerts pressure in all directions — on the bottom of its container, against the side walls, and on any object submerged within it Science, Class VIII NCERT, Pressure, Winds, Storms, and Cyclones, p.85. In physics, we define Pressure as the force acting per unit area (P = F/A), measured in Pascals (Pa) or Newtons per square metre (N/m²) Science, Class VIII NCERT, Pressure, Winds, Storms, and Cyclones, p.94. As you go deeper into a fluid, the weight of the fluid above increases, which in turn increases the pressure.

This difference in pressure at different depths is the birth of Upthrust (also known as Buoyant Force). Imagine a cube submerged in water: the water pressure pushing up on the bottom face is greater than the pressure pushing down on the top face because the bottom is deeper. This net upward force is what makes an empty plastic bottle 'bounce' back to the surface when you try to submerge it Science, Class VIII NCERT, Exploring Forces, p.76. Every liquid applies this upward force on objects placed within it, and its strength is governed by Archimedes' Principle: the upthrust is exactly equal to the weight of the fluid displaced by the object.

The Principle of Flotation is a specific application of this balance. For an object to float in equilibrium, the upward buoyant force must perfectly match the downward gravitational force (the object's weight). This explains a common paradox: why does a small steel nail sink while a massive steel ship floats? The ship is hollowed out to enclose a large volume of air, which reduces its average density. This allows the ship to displace a volume of water whose weight is equal to the entire ship's weight before it is fully submerged. If the object cannot displace enough water to match its own weight, it will sink.

Condition	Result	Physics Behind It
Weight > Upthrust	Sinks	Object is denser than the fluid; it cannot displace enough weight of fluid to balance itself.
Weight = Upthrust	Floats (Neutral)	Object is in equilibrium; the weight of displaced fluid equals the object's weight.

Sources: Science, Class VIII NCERT (Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.85; Science, Class VIII NCERT (Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.94; Science, Class VIII NCERT (Revised ed 2025), Exploring Forces, p.76

3. Gravitational Force and Weight in Equilibrium (basic)

To understand why massive ships float while a small needle sinks, we must first master the distinction between Mass and Weight. Mass represents the actual quantity of matter in an object and remains constant regardless of where you are in the universe Science, Class VIII, Chapter 9, p.142. Weight, however, is a force — specifically, the gravitational pull exerted on that mass by a planet Science, Class VIII, Chapter 5, p.75. Because weight is a force, it is measured in Newtons (N). In the context of Earth's gravity, an object with a mass of 225 kg experiences a weight (gravitational force) of approximately 2250 N Science, Class VIII, Chapter 7, p.87.

Feature	Mass	Weight
Definition	Quantity of matter in an object	Gravitational force pulling the object
SI Unit	Kilogram (kg)	Newton (N)
Nature	Constant everywhere	Changes based on local gravity

When an object is in static equilibrium, it means the forces acting upon it are perfectly balanced, resulting in no movement Science, Class VIII, Chapter 5, p.65. For a boat floating on water, two primary forces are in a tug-of-war: the downward force of Gravity (Weight) and the upward Buoyant Force provided by the water. According to Archimedes' Principle, this upward force is exactly equal to the weight of the fluid that the object displaces Science, Class VIII, Chapter 5, p.76.

The Principle of Flotation states that for any vessel to float, it must displace a weight of liquid equal to its own total weight. A solid block of steel sinks because its high density prevents it from displacing enough water to match its weight before it is fully submerged. However, a steel boat is engineered to be hollow, enclosing a large volume of air. This reduces the average density of the vessel, allowing it to displace a volume of water whose weight is equal to the boat's weight long before the boat sinks below the waterline Science, Class VIII, Chapter 5, p.76.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.65, 75, 76; 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 7: Pressure, Winds, Storms, and Cyclones, p.87

4. Connected Concept: Surface Tension (intermediate)

Have you ever noticed how a small insect can walk across a pond without sinking, or how dew drops on a leaf always seem to form perfect little beads? This happens because of a fascinating property called surface tension. To understand this from first principles, we must look at the interparticle forces of attraction between molecules. As we've seen in our study of the particulate nature of matter, particles in a liquid are constantly attracting one another Science, Class VIII. NCERT (Revised ed 2025), Particulate Nature of Matter, p.105.

Inside the bulk of a liquid, a molecule is surrounded by other molecules on all sides, pulling it equally in every direction. However, a molecule at the surface is different. It has neighbors to its sides and below it, but none above it. This creates an imbalance of forces, resulting in a net inward pull toward the center of the liquid. This inward pull makes the surface of the liquid contract and behave as if it were covered by a thin, stretched elastic membrane or "skin."

This "skin-like" behavior is why liquids try to occupy the smallest possible surface area. For a given volume, a sphere has the smallest surface area, which is why raindrops and soap bubbles are round. While we often think of liquids as needing atmospheric pressure to exist without evaporating away Physical Geography by PMF IAS, Earths Atmosphere, p.281, surface tension is the internal force that dictates how that liquid’s surface actually behaves once it is there. It is distinct from buoyancy; while buoyancy depends on displaced weight, surface tension depends on the cohesion of molecules at the boundary.

Feature	Molecules in the Bulk	Molecules at the Surface
Surrounding Neighbors	Attracted from all sides.	Attracted only from the sides and below.
Net Force	Zero (balanced).	Inward (toward the liquid).
Result	Stable movement.	Creation of surface tension.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Particulate Nature of Matter, p.105; Physical Geography by PMF IAS, Earths Atmosphere, p.281

5. Connected Concept: Viscosity and Fluid Drag (intermediate)

When we think of friction, we usually imagine two solid surfaces rubbing together, like your shoes on a pavement. However, friction is not limited to solids. In the world of physics, fluids (which include both liquids and gases) also exert a resistive force on objects moving through them. This fluid friction is commonly known as Drag. Just as the irregularities between two solid surfaces lock into each other to oppose motion Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.68, the molecules of a fluid interact with a moving object to slow it down.

To understand why some fluids resist motion more than others, we look at Viscosity. Think of viscosity as the "thickness" or the internal friction of the fluid itself. For instance, honey is more viscous than water, meaning its layers struggle to slide past one another. The amount of drag an object experiences depends on three main factors: the speed of the object, its shape, and the nature (viscosity) of the fluid. To minimize this drag, engineers and nature alike use "streamlining"—shaping objects like birds, fish, and airplanes to cut through fluids with minimal resistance.

A fascinating application of these principles is found in our atmosphere. Jet streams, which are high-speed winds in the upper troposphere, can reach speeds exceeding 400 kmph Physical Geography by PMF IAS, Jet streams, p.386. One reason they can maintain such incredible velocities is that the air in the upper troposphere is less dense. Thinner air means fewer molecules to collide with, resulting in significantly lower friction or drag compared to the air near the Earth's surface. Furthermore, the velocity of these streams is driven by temperature contrasts; the greater the temperature difference between air masses, the faster the flow Physical Geography by PMF IAS, Jet streams, p.385.

Factor	Effect on Fluid Drag
Velocity	Drag increases as the speed of the object through the fluid increases.
Fluid Density	Lower density (like high-altitude air) results in lower drag forces.
Shape	Streamlined shapes reduce drag; blunt shapes increase it.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.68; Physical Geography by PMF IAS, Jet streams, p.385-386

6. Archimedes' Principle Explained (intermediate)

Have you ever noticed how you feel significantly lighter while swimming in a pool? This isn't just a trick of the mind; it is a fundamental law of physics discovered by the Greek scientist Archimedes. Archimedes' Principle states that when an object is partially or fully immersed in a fluid (liquid or gas), it experiences an upward buoyant force that is exactly equal to the weight of the fluid it displaces Science, Class VIII . NCERT(Revised ed 2025), Chapter 5: Exploring Forces, p.76. This principle is the cornerstone of why massive ships stay afloat while a tiny pebble sinks to the bottom.

To understand why some objects float and others sink, we look at the competition between two forces: Gravity pulling the object down and Buoyancy pushing it up. This leads us to the Principle of Flotation. If the weight of the liquid displaced is less than the weight of the object, the object will sink. However, if the displaced liquid's weight is equal to the object's weight, it will float in equilibrium Science, Class VIII . NCERT(Revised ed 2025), Chapter 5: Exploring Forces, p.76. This explains the "Ship Paradox": a solid steel bar sinks because it is dense and cannot displace enough water to match its weight. In contrast, a steel ship is hollowed out to enclose air, drastically reducing its average density. This allows the ship to displace a volume of water whose weight equals the total weight of the ship before it sinks too deep.

Scenario	Force Comparison	Result
Sinking	Weight of Object > Buoyant Force	Object moves downward
Floating	Weight of Object = Buoyant Force	Object stays at surface/suspension
Rising	Weight of Object < Buoyant Force	Object moves upward (like a balloon)

Interestingly, this concept also explains why measuring weight in a fluid gives a lower reading than in air. If you use a spring balance to weigh an object submerged in water, the reading will decrease by exactly the weight of the water displaced Science, Class VIII . NCERT(Revised ed 2025), Chapter 5: Exploring Forces, p.74. This "apparent loss of weight" is simply the buoyant force lending a helping hand to support the object's mass.

Sources: Science, Class VIII . NCERT(Revised ed 2025), Chapter 5: Exploring Forces, p.76; Science, Class VIII . NCERT(Revised ed 2025), Chapter 5: Exploring Forces, p.74

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

Have you ever wondered why a small iron nail sinks instantly, while a massive steel ship carrying thousands of tons of cargo glides effortlessly across the ocean? This phenomenon is governed by the Law of Flotation, which is a direct application of Archimedes' Principle. This principle states that any object, partially or fully immersed in a fluid, experiences an upward buoyant force equal to the weight of the fluid it displaces Science, Class VIII NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.76. Interestingly, this concept of buoyancy is so fundamental that it was even used by early geologists to explain the movement of entire continents across the Earth's mantle Physical Geography by PMF IAS, Tectonics, p.95.

For a vessel to float in static equilibrium, the upward buoyant force must exactly balance the downward gravitational force (the boat’s weight). This leads us to the core rule: a floating object displaces a weight of liquid equal to its own weight. If you feel a bucket of water feels lighter when the mug is still submerged, you are experiencing this buoyant force in action Science, Class VIII NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.76. The challenge for engineers is ensuring that the object is shaped to displace enough water to match its weight before it sinks too deep.

The secret of ship design lies in Average Density. While a solid bar of steel is much denser than water and will sink, a ship is designed to be hollow, enclosing a vast volume of air. This massive increase in volume, without a proportional increase in mass, lowers the ship's average density to less than that of water. Because the hull is wide and deep, it can displace a huge volume of water; the weight of this displaced water provides the necessary buoyant force to keep the heavy steel structure and its cargo afloat.

Scenario	Weight vs. Buoyant Force	Result
Solid Steel Nail	Weight > Weight of displaced water	Sinks
Hollow Steel Ship	Weight = Weight of displaced water	Floats

Sources: Science, Class VIII NCERT (Revised ed 2025), Chapter 5: Exploring Forces, p.76; Physical Geography by PMF IAS, Tectonics, p.95

8. Solving the Original PYQ (exam-level)

To solve this question, we must synthesize two core concepts you have just mastered: Archimedes' Principle and the Principle of Flotation. You've learned that buoyancy is the upward force exerted by a fluid. When a boat floats, it is in a state of static equilibrium, meaning the downward force (the boat's gravity/weight) and the upward force (buoyancy) are perfectly balanced. According to Science, Class VIII, NCERT, for any object to stay afloat, the buoyant force must exactly negate the object's total weight.

Walking through the logic: if the boat is floating, then the Buoyant Force = Weight of the Boat. Since Archimedes' Principle states that the Buoyant Force = Weight of the fluid displaced, it logically follows that the weight of the water displaced by the boat is equal to the weight of the boat. This makes (D) the correct answer. The shape of the boat allows it to displace a large volume of water, ensuring that the weight of that displaced water matches the total weight of the steel and its cargo before the boat becomes fully submerged.

UPSC often uses distractors to test the precision of your conceptual clarity. Options (A) and (B) represent non-equilibrium states; if the displaced water weighed less than the boat, the boat would sink. Option (C) is a common conceptual trap; while the volume of the displaced water is equal to the volume of the boat submerged, the question asks for the weight. Always remember the fundamental rule of flotation: for any floating body, weight must balance weight.