The density of cast iron having specific gravity 7.20 is

1. Fundamentals of Matter: Mass and Volume (basic)

At its most fundamental level, physics defines matter as anything that has mass and occupies volume (space) Science, Class VIII, Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.140. While we often use these terms in daily life, in mechanics, they have very specific roles. Mass is a measure of the amount of 'stuff' or particles contained within an object, whereas volume is the three-dimensional space that those particles take up.

The relationship between these two properties gives us Density, which is defined as the mass present in a unit volume of a substance. Mathematically, it is expressed as:

Density = Mass / Volume

Whether a substance is a solid, liquid, or gas depends largely on how closely its particles are packed—this is known as interparticle spacing Science, Class VIII, Chapter: Particulate Nature of Matter, p.107. Solids typically have very small gaps between particles, making them more 'dense' compared to gases, where particles are far apart. Interestingly, while the shape or size of an object can change (a physical change), its density remains a characteristic property of the material itself, though it can be influenced by external factors like temperature and pressure Science, Class VII, Chapter: Changes Around Us: Physical and Chemical, p.59.

Concept	Definition	Common Units
Mass	The quantity of matter in an object.	Kilograms (kg), Grams (g)
Volume	The space occupied by an object.	Cubic meters (m³), Liters (L), cm³
Density	Mass per unit of volume.	kg/m³, g/cm³

Sources: Science, Class VIII, Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.140; Science, Class VIII, Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.150; Science, Class VIII, Particulate Nature of Matter, p.107; Science, Class VII, Changes Around Us: Physical and Chemical, p.59

2. Density: The Mass-Volume Relationship (basic)

In physics, density represents how much 'stuff' is packed into a specific amount of space. Imagine two identical boxes: one filled with feathers and the other with lead. Even though they occupy the same volume, the lead box is much heavier because its mass is higher. We define density as the mass per unit volume of a substance. It is an intrinsic property, meaning it doesn't change whether you have a tiny pebble or a massive boulder of the same material. As per scientific standards, the SI unit of density is the kilogram per cubic metre (kg/m³), though in laboratory settings, you will often see grams per cubic centimetre (g/cm³) or g/mL Science, Class VIII, Chapter 9, p.141.

Mathematically, we express this relationship as: Density = Mass / Volume. This concept is so fundamental that it extends beyond physics into human geography. For example, population density uses the same logic to measure how many people live in a specific area (Persons per sq km), helping us understand the 'crowdedness' of different regions Contemporary India-I, Geography, Class IX, Chapter 6, p.49. Whether we are discussing atoms in a metal or people in a city like Bihar, the core concept remains a ratio of 'quantity' to 'space'.

To make comparisons easier, scientists often use Specific Gravity (also known as Relative Density). This is the ratio of a substance's density to the density of a reference material—usually pure water at 4°C. Since water has a density of approximately 1000 kg/m³, it serves as a perfect baseline. Because specific gravity is a ratio of two similar quantities (density divided by density), it is a dimensionless number (it has no units). If a metal has a specific gravity of 7.20, it simply means it is 7.2 times more dense than water.

Sources: Science, Class VIII, Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.141; Contemporary India-I, Geography, Class IX, Chapter 6: Population, p.49

3. SI Units and Dimensional Analysis (intermediate)

In the world of physics and engineering, a number without a unit is like a traveler without a map—it has no direction or meaning. To ensure global consistency, we use the International System of Units (SI). At the foundational level, we deal with Base Units such as the metre (m) for length, the kilogram (kg) for mass, and the second (s) for time. Interestingly, symbols for units like 's' or 'min' are always written in lowercase and never end with a full stop unless they conclude a sentence Science-Class VII, Measurement of Time and Motion, p.111.

When we combine these base units, we get Derived Units. For instance, Speed is distance divided by time, giving us the SI unit m/s Science-Class VII, Measurement of Time and Motion, p.113. Similarly, Density—the amount of mass packed into a specific volume—is calculated as mass/volume. Since the SI unit for volume is the cubic metre (m³), the SI unit for density is kg/m³ Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.141. It is also vital to distinguish between mass (the amount of matter) and weight (the force of gravity acting on that matter); in SI, mass is measured in kg, while weight is measured in Newtons (N) Science, Class VIII, Exploring Forces, p.75.

Dimensional Analysis allows us to understand the nature of a physical quantity regardless of the specific units used. A fascinating case is Specific Gravity (also known as relative density). It is defined as the ratio of a substance's density to the density of a reference material (usually water). Because it is a ratio of two identical physical quantities (Density ÷ Density), the units cancel out entirely, making it a dimensionless quantity. To convert specific gravity back into a usable SI density, we simply multiply it by the density of water, which is approximately 1000 kg/m³. For example, if cast iron has a specific gravity of 7.20, its density in SI units is 7200 kg/m³.

Physical Quantity	SI Unit	Nature
Mass	kg	Base Unit
Density	kg/m³	Derived Unit
Specific Gravity	None	Dimensionless

Sources: Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.111, 113; Science ,Class VIII . NCERT(Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.141; Science ,Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.75

4. Archimedes' Principle and Buoyancy (intermediate)

Have you ever noticed how you feel significantly lighter when you step into a swimming pool? This isn't just an illusion; it is the result of Buoyancy (also called Upthrust). When any object is placed in a fluid, the fluid exerts an upward force that opposes the object's weight. This force is a fundamental concept in mechanics, as it determines whether a massive ship stays afloat or a tiny pebble sinks to the bottom Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.77.

To understand the exact strength of this force, we look to Archimedes' Principle. The principle states that when an object is fully or partially immersed in a liquid, the upward buoyant force is exactly equal to the weight of the liquid displaced by the object Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.76. This explains why a hollow iron ship floats while a solid iron nail sinks: the ship is shaped to displace a volume of water whose weight is equal to the ship's entire weight, creating enough upthrust to keep it at the surface.

The interaction between gravity and buoyancy creates three possible scenarios for any object in a liquid:

Scenario	Force Comparison	Outcome
Sinking	Gravitational Force (Weight) > Buoyant Force	The object moves downward to the bottom.
Floating (at surface)	Gravitational Force = Buoyant Force	The object stays at the surface or partially submerged.
Rising	Gravitational Force < Buoyant Force	The object is pushed upward until it reaches equilibrium at the surface.

Finally, we must consider Density and Specific Gravity. Density is mass per unit volume. In scientific calculations, we often use Specific Gravity (or relative density), which is the ratio of a substance's density to the density of water (usually at 4°C, where water is densest at approx. 1000 kg/m³) Science, Class VIII, NCERT (Revised ed 2025), How do scientists define density?, p.141. If a substance has a specific gravity greater than 1, it is denser than water and will likely sink; if less than 1, it will float.

Sources: Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.76; Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.77; Science, Class VIII, NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.141

5. Material Science: Properties of Cast Iron and Alloys (intermediate)

In the world of material science, iron is not a single uniform metal but a versatile family of materials categorized by their carbon content and physical properties. Cast Iron is an alloy of iron containing a high proportion of carbon (typically 2% to 4%), which makes it remarkably hard but also quite brittle. Unlike steel, which can deform under stress, cast iron tends to "snap" when subjected to sudden pressure, a quality often observed in historical lamp posts or heavy machinery bases Certificate Physical and Human Geography, Manufacturing Industry and The Iron and Steel Industry, p.285. In contrast, Wrought Iron is the purest form of commercial iron, known for being tough, resistant to rust, and malleable enough for ornamental gates Certificate Physical and Human Geography, Manufacturing Industry and The Iron and Steel Industry, p.285. To bridge the gap between pure iron and specific engineering needs, we use Alloys. An alloy is a homogeneous mixture of a metal with other elements to enhance its properties, such as increasing hardness or preventing corrosion Science Class X (NCERT 2025 ed.), Metals and Non-metals, p.55. For instance, Steel is created by carefully controlling carbon levels (0.3% to 2.2%) and adding ferro-alloys like Chromium for rust resistance or Manganese for strength Certificate Physical and Human Geography, Manufacturing Industry and The Iron and Steel Industry, p.285. From an engineering perspective, understanding a material's mass is as vital as its strength. This brings us to Specific Gravity (or relative density), a dimensionless number that compares the density of a material to the density of pure water at 4°C Science Class VIII (NCERT 2025 ed.), Chapter 9, p.141. Because the density of water is exactly 1000 kg/m³, calculating the actual density of a metal is straightforward. For Cast Iron, which has a standard specific gravity of 7.20, the density is calculated as:

Density = Specific Gravity × Density of Water = 7.20 × 1000 kg/m³ = 7200 kg/m³.

Material	Carbon Content	Primary Property
Cast Iron	High (2-4%)	Brittle; Snaps under pressure
Steel	Low to Mid (0.3-2.2%)	Elastic; Strong and Ductile
Wrought Iron	Very Low	Tough; Resists rust

Sources: Certificate Physical and Human Geography, Manufacturing Industry and The Iron and Steel Industry, p.284-285; Science Class X (NCERT 2025 ed.), Metals and Non-metals, p.55; Science Class VIII (NCERT 2025 ed.), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.141

6. Relative Density (Specific Gravity) (exam-level)

When we compare the density of a substance to a standard reference, we are measuring its Relative Density (also known as Specific Gravity). In most scientific and engineering contexts, the reference material used is pure water at 4°C. Why 4°C? Because that is the temperature at which water reaches its maximum density—exactly 1000 kg/m³ (or 1 g/cm³). By comparing a substance to water, we get a clear sense of how much "heavier" or "lighter" it is relative to a common medium. As defined in standard scientific literature, the relative density is the ratio of the density of a substance to the density of water at that same temperature Science, Class VIII . NCERT(Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.141.

One of the most important characteristics of Relative Density is that it is a dimensionless quantity. Since you are dividing density (kg/m³) by density (kg/m³), the units cancel out, leaving you with a pure number Science, Class VIII . NCERT(Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.141. This makes it incredibly useful for quick comparisons. For example, if a metal has a relative density of 7.2, it means it is 7.2 times as dense as water. To find its actual density in SI units, you simply multiply the relative density by the density of water:
Density of substance = Relative Density × 1000 kg/m³.

Understanding this concept is vital because density determines whether an object will sink or float. If the relative density is greater than 1, the substance is denser than water and will sink; if it is less than 1, it will float. In nature, these density differences drive massive systems; for instance, cold water is denser than warm water, and high-salinity water is denser than low-salinity water. These differences cause denser water to sink and lighter water to rise, creating the vertical and horizontal ocean currents that regulate our planet's climate 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.140-141; Physical Geography by PMF IAS, Ocean Movements Ocean Currents And Tides, p.487

7. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamental concepts of density and relative density, this question serves as a perfect bridge between theory and application. The building blocks you just learned—specifically the definition of specific gravity as a dimensionless ratio—are the key here. As discussed in Science, Class VIII, NCERT (Revised ed 2025), specific gravity compares a substance's density to a reference, which is almost always water at 4°C. To solve this, you must apply the bridge formula: Density of Substance = Specific Gravity × Density of Water.

Walking through the reasoning, we know the standard density of water is 1000 kg/m³ in SI units. By multiplying the given specific gravity of 7.20 by this constant (7.20 × 1000), we arrive at 7200 kg/m³. This simple multiplication shifts the value from a relative ratio to an absolute measurement of mass per unit volume. Therefore, Option (D) 7200 kg/m³ is the only logically and mathematically sound conclusion.

In the context of UPSC, it is vital to watch out for decimal traps and unit confusion. Option (A) 7.20 kg/m³ is a classic trap designed to catch students who forget that specific gravity is unitless and must be converted to reach a density value. Options (B) and (C) are distractors that test whether you remember the specific power of ten for water's density; if you mistakenly multiply by 10 or 100 instead of 1000, you fall into their target zone. Always verify your units and constants to avoid these common pitfalls.