A balloon filled up with gas would only go up in air if it is filled up with

1. Understanding Density: Mass per Unit Volume (basic)

Welcome to your first step in mastering basic mechanics! To understand how the physical world works—from why ships float to why clouds form—we must start with the concept of Density. At its simplest, density describes how much "stuff" (mass) is packed into a specific amount of space (volume). As defined in Science, Class VIII, NCERT (Revised ed 2025), Chapter 9, p.140, density is the mass present in a unit volume of a substance.

Mathematically, we express this as:

Density = Mass / Volume

An essential characteristic of density is that it is an intrinsic property. This means the density of a pure substance, like gold or iron, remains the same regardless of its shape or size Science, Class VIII, NCERT (Revised ed 2025), Chapter 9, p.140. If you have a large gold brick and a tiny gold earring, their density is identical because as the mass increases, the volume increases proportionally.

However, density is not strictly permanent; it changes with temperature and pressure. In most substances, when you heat them, the particles move faster and spread out, causing the volume to increase. Since the mass (the amount of matter) stays the same but the volume grows, the density decreases Science, Class VIII, NCERT (Revised ed 2025), Chapter 9, p.147. This is why hot air rises—it is less dense than the cooler air surrounding it.

Factor	Change	Effect on Density
Temperature	Increase (Heating)	Decreases (Volume expands)
Temperature	Decrease (Cooling)	Increases (Volume contracts)
Pressure (Gases)	Increase	Increases (Volume compressed)

Finally, we measure density using the SI unit of kilogram per cubic metre (kg/m³), though in a laboratory setting, you will often see g/cm³ or g/mL used for convenience Science, Class VIII, NCERT (Revised ed 2025), Chapter 9, p.141.

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; Science, Class VIII, NCERT (Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.147

2. Gravity vs. Upthrust: Introduction to Forces (basic)

To understand why objects like balloons rise or stones sink, we must first understand that a force is simply a push or a pull resulting from an interaction between objects Science, Class VIII, Exploring Forces, p.77. In the context of atmospheric flight or floating, two primary forces are locked in a constant 'tug-of-war': Gravity and Upthrust (also known as the buoyant force). Gravity is a non-contact force with which the Earth pulls every object toward its center. We measure the strength of this pull as the weight of the object Science, Class VIII, Exploring Forces, p.72. Since weight is a force, its SI unit is the newton (N) Science, Class VIII, Exploring Forces, p.65. On the other hand, Upthrust is the upward force exerted by a fluid (like air or water) on any object placed in it. According to Archimedes' principle, this upward force is equal to the weight of the fluid that the object displaces. Whether an object rises, sinks, or floats depends entirely on the balance between these two forces:

Scenario	Force Relationship	Result
Sinking	Gravity > Upthrust	The object's weight is greater than the weight of the displaced fluid.
Rising	Upthrust > Gravity	The object is lighter than the fluid it displaces (e.g., a helium balloon).
Floating/Hovering	Upthrust = Gravity	The forces are balanced, and the object remains at a constant level.

For a balloon to ascend, we must make it 'lighter' than the air it replaces. This is achieved by filling the balloon with low-density gases like helium or hydrogen, or by heating the air inside the balloon. Heating air causes it to expand, increasing its volume and decreasing its density relative to the cooler ambient air Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.147. When the total weight of the balloon (including the envelope and the gas inside) becomes less than the weight of the displaced outside air, the upward buoyancy overcomes gravity, and the balloon takes flight.

Sources: Science, Class VIII (NCERT 2025), Exploring Forces, p.65, 72, 77; Science, Class VIII (NCERT 2025), The Amazing World of Solutes, Solvents, and Solutions, p.147

3. Structure of the Atmosphere and Pressure Gradients (intermediate)

To understand how objects move through our air, we must first look at the structure of the atmosphere as a physical medium. The atmosphere is not just "empty space"; it is a complex mixture of gases (chiefly Nitrogen and Oxygen), water vapor, and dust particles FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Composition and Structure of Atmosphere, p.64. Because of gravity, the atmosphere is densest near the surface and thins out rapidly as we move upward. In fact, the proportion of gases changes so significantly that oxygen becomes negligible at a height of 120 km, and CO₂ or water vapor are rarely found beyond 90 km FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Composition and Structure of Atmosphere, p.64.

This layering creates a vertical pressure gradient. Atmospheric pressure is essentially the weight of the air column above a point. As you ascend, there is less air above you, so pressure decreases—on average at a rate of about 1 mb for every 10 metres of elevation in the lower atmosphere FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Atmospheric Circulation and Weather Systems, p.76. Interestingly, while this vertical pressure gradient is much stronger than the horizontal gradients that cause surface winds, we aren't "blown upward" into space because this force is almost perfectly balanced by the downward pull of gravity FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Atmospheric Circulation and Weather Systems, p.76.

The mechanics of buoyancy depend entirely on these density and pressure differences. According to Archimedes' principle, any object immersed in a fluid (like air) experiences an upward buoyant force equal to the weight of the fluid it displaces. For a balloon to rise, the total weight of the balloon and the gas inside must be less than the weight of the displaced ambient air. This is why we use "lifting gases" like Helium or Hydrogen, which are much less dense than the nitrogen-oxygen mix of our atmosphere. Alternatively, hot air balloons achieve the same effect by heating air; as air molecules heat up, they move faster and spread out, decreasing the density relative to the cooler, heavier air outside.

Factor	Effect on Atmospheric Pressure
Altitude	Pressure decreases rapidly as height increases.
Temperature	Heating air decreases its density, leading to lower local pressure.
Water Vapour	Higher humidity (more water vapour) actually makes air less dense than dry air.

Sources: FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Composition and Structure of Atmosphere, p.64, 66; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Atmospheric Circulation and Weather Systems, p.76; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.305

4. Thermodynamics: Effect of Temperature on Gas Density (intermediate)

To understand why air moves the way it does, we must look at the fundamental relationship between mass, volume, and density. Density is defined as the mass of a substance per unit of volume (Density = Mass/Volume). In a gas, the particles are not fixed in place; they move freely and are highly sensitive to changes in energy. When we heat a gas, we are essentially giving these particles more kinetic energy. As they move faster, they collide more forcefully and push each other further apart. This causes the gas to expand, increasing its volume while the total mass remains exactly the same Science, Class VIII NCERT (Revised ed 2025), Chapter 9, p.147.

Because the same amount of matter (mass) is now spread over a larger space (increased volume), the density of the gas decreases. This is a crucial principle: generally, the density of a substance decreases with heating and increases with cooling Science, Class VIII NCERT (Revised ed 2025), Chapter 9, p.147. In the atmosphere, when a specific air parcel receives more heat than the surrounding air, it becomes less dense than its environment. This density imbalance creates an upward force, causing the lighter air parcel to rise—a process central to both weather patterns and the flight of hot air balloons Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.297.

Property	Heated Gas	Cooled Gas
Particle Motion	Fast, spreading apart	Slow, moving closer
Volume	Increases (Expansion)	Decreases (Contraction)
Density	Decreases (Lighter)	Increases (Heavier)

It is also important to note that as this warm air parcel rises, the ambient pressure around it drops because the atmosphere becomes thinner at higher altitudes. According to gas laws, this fall in external pressure allows the parcel to expand even further. This relationship between temperature, pressure, and volume is the heartbeat of thermodynamics in our atmosphere Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.297.

Sources: Science, Class VIII NCERT (Revised ed 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.147; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.297

5. Properties of Lifting Gases: Helium, Hydrogen, and Vapour (intermediate)

To understand why certain objects float in the sky while others fall, we must return to the first principles of Archimedes' Principle. This principle states that any object, whether a ship in water or a balloon in the sky, is pushed upward by a buoyant force equal to the weight of the fluid it displaces. For a balloon to rise, the total weight of the envelope, the payload, and the gas inside must be less than the weight of the displaced air. This is why we use "lifting gases"—gases that have a significantly lower density than the nitrogen-oxygen mixture that makes up our atmosphere NCERT Science (Revised 2025), Chapter 9, p.147.

In the natural layers of our atmosphere, gravity sorts gases by their weight. The lightest elements, Hydrogen (H₂) and Helium (He), are found in the highest concentrations in the heterosphere and exosphere, thousands of kilometers above the Earth Environment and Ecology by Majid Hussain, BASIC CONCEPTS, p.6. Because these gases are so light, they are prone to atmospheric escape, where they achieve enough velocity to leak into outer space Physical Geography by PMF IAS, Earths Atmosphere, p.280. For human use in ballooning, Hydrogen offers the greatest lift but is dangerously flammable. Helium, while slightly heavier and much rarer—comprising only 0.0005% of the atmosphere—is the preferred choice for weather balloons and blimps because it is chemically inert and safe Physical Geography by PMF IAS, Earths Atmosphere, p.271.

Lifting Medium	Pros	Cons
Hydrogen (H₂)	Lightest gas; provides maximum lift.	Highly flammable and explosive.
Helium (He)	Non-flammable (safe); second lightest.	Expensive and rare.
Hot Air	Renewable; easy to control (heating/cooling).	Requires constant fuel; lower lifting capacity.

A fascinating scientific nuance is the role of Water Vapour (H₂O). Counter-intuitively, water vapour is actually lighter than dry air. A molecule of water has a molecular mass of about 18, whereas the molecules in dry air (mostly N₂) have a mass of about 28. This means that humid air is less dense than dry air Physical Geography by PMF IAS, Hydrological Cycle, p.326. However, we don't use steam or vapour to lift balloons because as the balloon rises into the colder upper atmosphere, the vapour would condense into liquid water, adding weight and destroying the lift. This is why high-altitude flight relies on "permanent" light gases or the continuous heating of air to maintain low density.

Sources: NCERT Science (Revised 2025), Chapter 9: The Amazing World of Solutes, Solvents, and Solutions, p.147; Environment and Ecology by Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.6; Physical Geography by PMF IAS, Earths Atmosphere, p.271, 280; Physical Geography by PMF IAS, Hydrological Cycle (Water Cycle), p.326

6. Archimedes' Principle and the Law of Floatation (exam-level)

Have you ever noticed how you feel lighter while swimming, or how a heavy iron ship manages to stay afloat while a tiny nail sinks? This phenomenon is governed by the Buoyant Force (also known as Upthrust). When any object is placed in a liquid, two opposing forces act upon it: the gravitational force pulling it downward and the buoyant force applied by the liquid pushing it upward Science, Class VIII, Exploring Forces, p.76. The SI unit for both these forces is the Newton (N) Science, Class VIII, Exploring Forces, p.77.

The definitive rule for this upward push was discovered 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, Exploring Forces, p.76. This principle is not limited to water; it applies to all fluids, including the air around us. For instance, a balloon rises in the atmosphere because it displaces a volume of air that weighs more than the balloon itself. This is achieved by filling the balloon with gases like helium or hydrogen, which have a lower density than the surrounding air, or by heating the air inside to decrease its density Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.147.

Whether an object sinks or floats depends on the balance between its weight and the buoyant force. This is known as the Law of Floatation. If the weight of the object is greater than the buoyant force, it sinks. If they are equal, the object floats. This balance is fundamentally tied to density—the mass per unit volume of a substance. An object floats if its overall density is less than or equal to the density of the liquid it is in Science, Class VIII, Exploring Forces, p.76.

Scenario	Force Relationship	Outcome
Weight > Buoyant Force	Downward force wins	Object Sinks
Weight = Buoyant Force	Forces are balanced	Object Floats
Weight < Max Buoyant Force	Upward force wins	Object Rises (until forces balance)

Sources: Science, Class VIII, Exploring Forces, p.76; Science, Class VIII, Exploring Forces, p.77; Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.147

7. Solving the Original PYQ (exam-level)

This question perfectly synthesizes the concepts of density and Archimedes' Principle that you have just mastered. To solve this, you must view the atmosphere not just as empty space, but as a fluid medium. Just as a piece of cork floats in water because it is less dense, a balloon rises because the buoyant force (the weight of the air displaced) is greater than the gravitational weight of the balloon and its internal gas. This requires the total mass of the gas inside to be significantly less than the mass of the same volume of surrounding air, leading us directly to (A) a gas whose density is lower than air.

As a UPSC aspirant, you must learn to think in terms of differentials. When you see options like (B) or (C), recognize them as common 'reversal traps.' A gas with a higher density or cold air (which is more compact and heavy) would increase the balloon's weight, causing it to sink rather than rise. While water vapour (D) is technically less dense than dry air, it is an impractical choice due to condensation; the question asks for the fundamental condition that enables ascent, which is always the density gradient. This principle is further detailed in Science, Class VIII, NCERT, where the effect of temperature on density explains how even hot air balloons function by creating a low-density environment inside the envelope.