The following blocks are of the same material. Which is the heaviest one ?

1. Foundations of Matter: Mass vs. Weight (basic)

In our daily lives, we often use the words mass and weight interchangeably. We might say a bag of wheat "weighs" 10 kg, but in the world of physics, this is technically a mix-up of two very different concepts. Mass is an intrinsic property of an object; it represents the actual quantity of matter contained within it Science, Class VIII, NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.142. Whether you are on Earth, on the Moon, or floating in deep space, your mass remains exactly the same because the amount of "stuff" you are made of hasn't changed.

Weight, on the other hand, is a force. Specifically, it is the gravitational pull exerted by a massive body (like the Earth) on an object Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.75. Because weight depends on gravity, it is variable. If you travel to the Moon, where gravity is much weaker, you would weigh much less, even though your mass remains identical. This is why weight is measured in Newtons (N), the standard unit for force, while mass is measured in kilograms (kg) or grams (g) Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.77.

When comparing objects made of the same material (same density), the one with more volume will contain more matter, meaning it has more mass. Since weight is directly proportional to mass (Weight = Mass × Gravity), the object with the greatest mass will also be the heaviest in any given gravitational field. Most scales we use daily are actually measuring this downward pull (weight) but are calibrated to show us the value in kilograms for our convenience Science, Class VIII, NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.142.

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Force of gravity acting on an object.
SI Unit	Kilogram (kg)	Newton (N)
Variability	Constant everywhere.	Changes based on local gravity.

Sources: Science, Class VIII, NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.142; Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.75, 77

2. Understanding Material Density (basic)

To understand the physical world, we must first understand Density—a fundamental property that tells us how "compact" a substance is. In simple terms, density is the amount of mass present in a specific unit volume of a substance Science, Class VIII . NCERT(Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.140. Imagine two identical boxes: one filled with feathers and the other with lead. Even though they occupy the same space (volume), the lead box is much heavier because its particles are packed much more tightly. That "tightness" is what we call density.

Mathematically, density is expressed by the following formula:

Density = Mass / Volume

One of the most important things to remember for competitive exams is that density is an intrinsic property. This means the density of a pure substance (like gold or iron) remains the same regardless of its size or shape Science, Class VIII . NCERT(Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.140. Whether you have a tiny gold ring or a large gold brick, the density of gold is constant. However, factors like temperature and pressure can cause density to change, especially in gases where particles can be easily squeezed together or expanded.

When we compare different materials, we often use Relative Density. This is a unitless number that compares 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.141. If we know that two objects are made of the same material, their densities are identical. In such cases, the object with the larger volume will naturally have a higher mass (and thus be heavier), because mass is simply the product of density and volume (Mass = Density × Volume).

Sources: Science, Class VIII . NCERT(Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.140; Science, Class VIII . NCERT(Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.141

3. Geometry in Science: Calculating Volume (basic)

In our journey through mechanics, we must transition from looking at objects as mere points to understanding them as physical bodies that occupy space. This space is called Volume. While area measures a flat surface, volume accounts for the third dimension—depth or height. Whether you are looking at a buttermilk tetra pack or a stone, the volume tells us exactly how much "room" that object takes up in the universe Science Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.143.

For regular geometric shapes like cuboids (think of a brick, a notebook, or a shipping container), calculating volume is a matter of simple multiplication. We measure three distinct dimensions: Length (l), Width (w), and Height (h). The formula is expressed as:

Volume = l × w × h

As noted in Science Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.145, if you measure a notebook with a length of 25 cm, width of 18 cm, and height of 2 cm, its volume would be 900 cubic centimetres (cm³).

Understanding the units of volume is crucial for scientific precision. While the standard SI unit is the cubic metre (m³), we often use smaller units in daily life and laboratory settings. A helpful rule of thumb is that for solids, we typically use cm³ (sometimes called cc), while for liquids, we use millilitres (mL) or litres (L). Remarkably, these scales are perfectly aligned: 1 cm³ is equivalent to 1 mL Science Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.146.

Unit	Common Use Case	Equivalency
Cubic Metre (m³)	Large spaces (rooms, water tanks)	1000 Litres
Litre (L)	Liquid quantities (milk, fuel)	1 dm³
Cubic Centimetre (cm³)	Small solids or engine capacity	1 mL

Sources: Science Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.143; Science Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.145; Science Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.146

4. Connected Concept: Archimedes' Principle and Buoyancy (intermediate)

Have you ever noticed how a heavy bucket of water feels strangely light while it is still submerged, only to become much heavier the moment it breaks the surface? This phenomenon is driven by a fundamental force called Buoyancy. As explained in Science, Class VIII, Exploring Forces, p.76, whenever an object is placed in a liquid, the liquid exerts an upward force on it. This is why you might feel a sense of weightlessness in a swimming pool; the water is literally helping to carry your weight.

To understand exactly how much help the water provides, we look to Archimedes' Principle. This principle states that when an object is fully or partially immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces. Imagine dropping a stone into a glass filled to the brim; the water that spills out is the "displaced" liquid. If that spilled water weighs 2 Newtons, then the upward buoyant force acting on the stone is exactly 2 Newtons.

Whether an object sinks or floats depends on the tug-of-war between two forces: the downward pull of gravity (the object's weight) and the upward push of buoyancy. As noted in Science, Class VIII, Exploring Forces, p.76:

• Sinking: If the weight of the displaced liquid is less than the weight of the object, the object sinks.
• Floating: If the weight of the displaced liquid is equal to the weight of the object, the object floats.

This explains why a heavy iron rod sinks while a lighter wooden stick of the same size might float (Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.140). It also explains why density matters; objects like oil float on water because they are less dense, meaning a specific volume of oil weighs less than the same volume of water, allowing the water's buoyant force to easily overcome the oil's weight.

Sources: Science, Class VIII, Exploring Forces, p.76; Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.140

5. Connected Concept: Newton’s Laws and Force (intermediate)

To understand how objects move or stay still, we must first master the relationship between Mass, Weight, and Force. In physics, a Force is defined as a push or a pull on an object resulting from its interaction with another object Science, Class VIII. NCERT(Revised ed 2025), Exploring Forces, p.77. This interaction can be a physical touch (contact force) or happen at a distance, like gravity (non-contact force). According to Newton’s Second Law, the force acting on an object is the product of its mass and its acceleration (F = ma). When we talk about "weight," we are actually talking about the gravitational force pulling an object toward the center of a planet.

It is vital to distinguish between Mass and Weight. Mass is the amount of matter in an object and remains constant regardless of where you are in the universe. Weight, however, is a force and changes depending on the local strength of gravity. For instance, your weight on the Moon would be much less than on Earth because the Moon's surface gravity is only about 1.62 m/s² compared to Earth’s 9.8 m/s² Physical Geography by PMF IAS, The Solar System, p.23. Interestingly, gravity is not even uniform across Earth; it is slightly stronger at the poles and weaker at the equator because the Earth is not a perfect sphere FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19.

In many practical problems, we aren't given the mass directly; instead, we are given the Volume (the space an object occupies) and the material it is made of. The link between them is Density. If two objects are made of the same material, they have the same density. Since Mass = Density × Volume, the object with the larger volume will have a greater mass. Consequently, because Weight = Mass × Gravity, the larger object will also be the heaviest, provided the material and the location remain the same.

Concept	Definition	SI Unit
Mass	Quantity of matter (intrinsic property)	Kilogram (kg)
Weight	Force of gravity acting on mass	Newton (N)
Density	Mass per unit volume	kg/m³

Sources: Science, Class VIII. NCERT(Revised ed 2025), Exploring Forces, p.77; Physical Geography by PMF IAS, The Solar System, p.23; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19

6. The Mass-Volume Proportionality Rule (exam-level)

To understand why some objects feel heavier than others despite being made of the same material, we must look at the Mass-Volume Proportionality Rule. At its core, mass is the amount of matter contained within an object Science, Class VIII, Exploring Forces, p.75. However, mass doesn't exist in a vacuum; it occupies space, which we call volume. The bridge between these two concepts is density—a measure of how tightly that matter is packed. Mathematically, this is expressed as: Mass = Density × Volume.

When we compare objects made of the same material (such as three different blocks of wood or iron), their density remains constant. Because the density is the same, the mass becomes directly proportional to the volume. This means if you double the volume of a material, you lead to a doubling of its mass. In practical everyday scenarios on Earth, we often find mass by measuring weight, as weight is simply the force of gravity acting on that mass Science, Class VIII, Exploring Forces, p.75. Therefore, for objects of the same material, the one with the largest physical volume will naturally be the heaviest.

Calculating this relationship is straightforward for regular geometric shapes. By multiplying the dimensions (Length × Width × Height), we find the volume. As seen in density calculations for substances like water or aluminum, knowing the volume allows us to predict the mass if the density is known Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.141. This rule is a fundamental principle in engineering and logistics: to reduce weight without changing the material, one must reduce the volume.

Scenario	Density	Relationship
Different Materials	Variable	Mass depends on both Density and Volume.
Same Material	Constant	Mass is directly proportional to Volume.

Sources: Science, Class VIII, Exploring Forces, p.75; Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.141

7. Solving the Original PYQ (exam-level)

Now that you have mastered the relationship between Density, Volume, and Mass, this question serves as the perfect practical application of those building blocks. The core principle at play here is that when the material is identical, the Density remains constant. As you learned in NCERT Class 9 Science, weight is directly proportional to volume in this scenario. Therefore, your task shifts from a complex physics problem to a straightforward Mensuration exercise: to find the heaviest block, you simply need to identify which one occupies the most space.

Let's walk through the mental math just as you would during the CSAT. To determine the volume, you must multiply the dimensions (Length × Width × Height) for each block. For Block A, the volume is 3 × 3 × 3 = 27 cubic units. For Block B, it is 4 × 3 × 2 = 24 cubic units. Finally, for Block C, the calculation 5 × 3 × 2 yields 30 cubic units. Since 30 is the highest numerical value, Option (C) is logically and mathematically the correct answer. This systematic approach ensures you aren't guessing based on how "big" a shape looks on paper.

UPSC often includes "traps" to test your confidence. Option (A) is a visual trap; because it is a perfect cube, it often appears more "solid" or "substantial" to the eye. Option (D) is a classic distractor designed to make you question your calculations, tempting you to believe there is a hidden trick where all volumes cancel out. Avoid the temptation to rely on visual intuition alone. In the CSAT, precision through calculation will always outperform perception. Always rely on the formula Mass = Density × Volume to ground your reasoning.