A piece of paper and a coin both having the same mass are dropped from the 10th floor of a building. The piece of paper would take more time to reach the ground because.

1. Newton’s Law of Universal Gravitation (basic)

At its heart, Newton’s Law of Universal Gravitation tells us that every single object in the universe that has mass exerts a pull on every other object. This isn't just a rule for planets or stars; it applies to the phone in your hand and the chair you're sitting on. Unlike magnetic or electrostatic forces, which can push things away (repulsion), the gravitational force is strictly attractive — it only pulls objects together Science, Class VIII, Exploring Forces, p.72. Because this force acts even when objects are not touching, we classify it as a non-contact force.

While the law is universal, we often use the term gravity to describe the specific pull exerted by the Earth on objects near its surface Science, Class VIII, Exploring Forces, p.72. We measure this pull as 'weight' using devices like a spring balance, which records the force in newtons (N) Science, Class VIII, Exploring Forces, p.73. It is important to remember that gravity is not uniform across the entire planet. Because the Earth is not a perfect sphere, the surface at the equator is further from the center than the surface at the poles. Consequently, gravitational pull is stronger at the poles and weaker at the equator Fundamentals of Physical Geography, Class XI, The Origin and Evolution of the Earth, p.19.

Furthermore, the mass of the material beneath the surface isn't distributed evenly. Places with denser material exert a slightly stronger pull. Scientists call these variations gravity anomalies, and they use these readings to map the distribution of mass within the Earth’s crust Physical Geography by PMF IAS, Earth's Interior, p.58. In simple mathematical terms, the force (F) depends on the masses of the two objects (m₁ and m₂) and the distance (r) between them: F = G(m₁m₂ / r²), where G is the universal gravitational constant.

Feature	Gravitational Force	Magnetic/Electrostatic Force
Nature	Always Attractive	Attractive or Repulsive
Requirement	Requires Mass	Requires Charge or Polarity
Contact	Non-contact	Non-contact

Sources: Science, Class VIII (NCERT 2025), Exploring Forces, p.72-73; Fundamentals of Physical Geography, Class XI (NCERT 2025), The Origin and Evolution of the Earth, p.19; Physical Geography by PMF IAS, Earth's Interior, p.58

2. Understanding Mass vs. Weight (basic)

To master mechanics, we must first distinguish between what an object is and how it interacts with the world. Mass is an intrinsic property of an object; it represents the actual quantity of matter present within it Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.142. Whether you take a gold bar to the peak of Mt. Everest or the vacuum of deep space, its mass remains identical because the amount of 'stuff' inside it hasn't changed. We measure mass in grams (g) or kilograms (kg).

Weight, however, is a force. Specifically, it is the gravitational pull exerted by a celestial body (like Earth) on an object Science, Class VIII, Exploring Forces, p.72. Because weight is a force, its SI unit is the Newton (N), not the kilogram. This is why your weight would change if you stood on the Moon—the Moon is less massive than Earth and pulls on you with less force, even though your body's mass remains exactly the same Science, Class VIII, Exploring Forces, p.75.

In our daily lives, we often use these terms interchangeably. For instance, a shopkeeper might say a bag of flour 'weights' 5 kg. Scientifically, 5 kg is its mass; its weight on Earth would actually be approximately 50 N (calculated as mass × gravity). We typically use a spring balance to measure weight, as the internal spring stretches in response to the downward pull of gravity Science, Class VIII, Exploring Forces, p.74.

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Force of gravitational attraction.
SI Unit	Kilogram (kg)	Newton (N)
Variability	Constant everywhere.	Changes based on local gravity.
Measurement Tool	Two-pan balance / Digital balance	Spring balance

Sources: Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.142; Science, Class VIII, Exploring Forces, p.72; Science, Class VIII, Exploring Forces, p.74; Science, Class VIII, Exploring Forces, p.75

3. Motion in a Vacuum: Galileo's Principle (intermediate)

For nearly two millennia, the world followed the Aristotelian view that heavier objects fall faster than lighter ones. Galileo Galilei challenged this through a revolutionary approach: he looked past the messy reality of air and friction to imagine how objects would behave in an "ideal" environment—a vacuum. Galileo realized that while the force of gravity is greater on a heavier object, that object also possesses more inertia (resistance to change in motion), which perfectly balances out the extra pull. Consequently, he proposed that all objects, regardless of their mass, fall with the same acceleration when air resistance is removed.

Because accurate clocks didn't exist in the 16th century, Galileo used ingenious methods to test his theories. He observed the rhythmic swinging of lamps in a cathedral, using his own pulse to measure time (Science-Class VII, Measurement of Time and Motion, p.108). By experimenting with pendulums, he discovered that the time it takes for one swing (the period) depends on the length of the string, not the mass of the bob (Science-Class VII, Measurement of Time and Motion, p.110). This supported his broader principle: gravity acts on the "essence" of the motion itself, independent of how much material is being moved.

Feature	Aristotelian View (Old)	Galilean Principle (Modern)
Falling Speed	Proportional to weight.	Same for all objects (in a vacuum).
Role of Medium	The medium (air/water) is necessary for motion.	The medium is a resistance that hides true laws of motion.
Key Discovery	Heavy things fall fast.	Acceleration due to gravity is a constant (g).

In our daily lives, we see a feather drift slowly while a stone drops quickly. This isn't because Galileo was wrong; it's because we live in a fluid (air). The air exerts an upward buoyant force and drag (air resistance). For a light, spread-out object like a feather, these upward forces are significant enough to counteract gravity. However, in a true vacuum chamber—or on the surface of the Moon—the feather and the stone would strike the ground at the exact same moment. This shift from observing "what happens" to understanding "why it happens" marks the birth of modern experimental science (History, class XII (Tamilnadu state board 2024 ed.), Modern World: The Age of Reason, p.134).

Sources: Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.108; Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.110; History , class XII (Tamilnadu state board 2024 ed.), Modern World: The Age of Reason, p.134

4. Archimedes' Principle and Upthrust (intermediate)

To understand why some objects float while others sink, we must look at the invisible tug-of-war happening inside a fluid. Whenever an object is placed in a liquid or gas, it experiences upthrust (also known as buoyant force). You can feel this yourself by trying to push an empty plastic bottle into a bucket of water—the water pushes back with a force directed upward, opposing gravity Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.76. This force is universal; all liquids and gases apply upthrust to objects immersed in them.

The magnitude of this force is governed by Archimedes' Principle. It states that the upward force (upthrust) acting on an object is exactly equal to the weight of the fluid the object displaces Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.76. This is why a massive steel ship can float while a small steel nail sinks. The ship is shaped to displace a huge volume of water, creating an upthrust equal to its weight. The nail, being compact, displaces very little water, so the upthrust is too weak to stop it from sinking.

Whether an object sinks or floats depends on the balance between two forces:

• Weight (Downward): Calculated as mass × gravity (mg). While mass is constant, weight can vary slightly depending on local gravity Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.77.
• Upthrust (Upward): Calculated as the weight of the displaced fluid.

Condition	Result	Physical Reason
Weight > Upthrust	Object Sinks	The object is denser than the fluid; it cannot displace enough fluid to match its own weight.
Weight = Upthrust	Object Floats	The object displaces a weight of fluid exactly equal to its own weight.

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

5. Fluid Dynamics: Viscosity and Drag (intermediate)

When we think of friction, we usually imagine two solid surfaces rubbing together. However, in fluid dynamics, we must account for the fact that gases (like air) and liquids (like water) also exert resistive forces on objects moving through them. This resistance is known as drag or fluid friction. While gravity pulls an object downward with a force equal to its mass times the gravitational constant (F = mg), the fluid pushes back with two primary upward forces: buoyancy and drag. According to Science Class VIII, NCERT, Exploring Forces, p.68, the shape of an object is crucial because it determines how much air or water resistance it encounters. This is why airplanes and high-speed trains are "streamlined"—designed specifically to minimize this opposing force.

The magnitude of these upward forces depends heavily on the physical properties of the object and the fluid. Buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object; it is directly proportional to the volume of the fluid displaced Science Class VIII, NCERT, Exploring Forces, p.76. Drag, on the other hand, depends on the object's speed, its cross-sectional area, and the fluid's viscosity (its "thickness" or resistance to flow). Even if two objects have the same mass, if one is spread out (like a flat sheet of paper) and the other is compact (like a metal coin), the spread-out object will experience a much higher drag force because it must push more air molecules out of its way to descend.

Force	Direction	Key Determinant
Gravity	Downward	Mass of the object
Buoyancy	Upward	Volume of the object (displaced fluid)
Drag (Friction)	Opposite to motion	Surface area, shape, and velocity

In the context of atmospheric science, these forces are part of a complex balance. Factors like the pressure gradient force and buoyant force dictate how air parcels move vertically and horizontally Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306. When the upward forces (drag + buoyancy) eventually equal the downward force of gravity, an object stops accelerating and falls at a constant speed known as terminal velocity. Because a sheet of paper has a high surface-area-to-mass ratio, its drag force equals its weight much sooner than a coin's does, leading to a much slower descent.

Sources: Science Class VIII, NCERT, Exploring Forces, p.68, 76; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306

6. Terminal Velocity and Net Force (exam-level)

When an object falls through a medium like air or water, it is not merely under the influence of gravity. Instead, it exists in a constant state of 'tug-of-war' between downward and upward forces. The downward force is Gravity (Weight = mg), which is constant for a given mass. Opposing this are two primary upward forces: Buoyant Force and Fluid Friction (often called air resistance or drag). As discussed in Science, Class VIII, NCERT, Exploring Forces, p.76, even when an object is in water or air, it experiences an upward push that can make it feel lighter; this is buoyancy, and it is proportional to the volume of the fluid displaced by the object. As the object accelerates downward due to gravity, its velocity increases. This is where Fluid Friction comes into play. Air and water exert a frictional force on objects moving through them, and this force increases as the object's speed increases Science, Class VIII, NCERT, Exploring Forces, p.68. Eventually, the speed becomes high enough that the sum of the upward forces (Drag + Buoyancy) exactly equals the downward force of Gravity. At this precise moment, the Net Force becomes zero. According to Newton's laws, if the net force is zero, the object stops accelerating and continues to move at a constant speed known as Terminal Velocity. The shape and surface area of an object significantly influence how quickly it reaches this state. For instance, objects with a larger surface area or a lower density (displacing more fluid relative to their mass) experience greater upward forces much sooner. This is why engineers design aeroplanes and high-speed trains with streamlined shapes to minimize this drag Science, Class VIII, NCERT, Exploring Forces, p.68. In contrast, a parachute is designed to maximize surface area, increasing drag to ensure a low terminal velocity for a safe landing.

Force Type	Direction	Dependency
Gravity	Downward	Mass of the object
Buoyancy	Upward	Volume of the object (displaced fluid)
Drag (Friction)	Upward	Speed, Shape, and Surface Area

Sources: Science, Class VIII, NCERT, Exploring Forces, p.68; Science, Class VIII, NCERT, Exploring Forces, p.76

7. Density-Volume Relationship in Buoyancy (exam-level)

To understand why objects behave differently when falling or floating, we must look at the interplay between density, volume, and the buoyant force. In physics, any fluid (which includes both liquids and gases) exerts an upward force on an object immersed in it. This is known as upthrust or buoyant force Science, Class VIII . NCERT, Exploring Forces, p.77. While gravity pulls an object down based on its mass, the fluid pushes it back up based on how much space (volume) the object occupies.

The relationship is governed by a fundamental formula: Density = Mass / Volume. This means that for a fixed amount of mass, density and volume are inversely proportional. If you have two objects with the identical mass—say, a gram of lead and a gram of feathers—the lead is much denser and occupies a tiny volume, whereas the feathers are less dense and occupy a much larger volume Science, Class VIII . NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.147. Because the buoyant force is directly proportional to the volume of fluid displaced, the object with the larger volume (and lower density) will experience a significantly stronger upward force from the surrounding air or water.

This principle explains many phenomena in our atmosphere. For example, when air is heated, its particles spread out, increasing its volume and decreasing its density. Because this warm air now occupies more space for its mass, the surrounding cooler air exerts a stronger buoyant force on it, causing the warm air to rise Science, Class VIII . NCERT, The Amazing World of Solutes, Solvents, and Solutions, p.147. Similarly, in geography, we see that low-pressure cells rise because the surrounding atmosphere exerts a buoyant force on them, while denser, high-pressure air tends to sink Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306.

When comparing two objects of equal mass falling through the air, the one with the lower density will have a larger surface area and volume. Consequently, it "pushes" against more air molecules, and the air "pushes back" with a greater upward buoyant force and resistance, slowing its descent compared to the denser, more compact object.

Feature	High Density Object (e.g., Metal)	Low Density Object (e.g., Paper/Air)
Volume (for same mass)	Small / Compact	Large / Expanded
Fluid Displacement	Low displacement	High displacement
Buoyant Force	Weak upward push	Strong upward push

Sources: 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.147; Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.), Pressure Systems and Wind System, p.306

8. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamentals of gravitational force and fluid mechanics, this question brings those building blocks together to test your conceptual clarity. While gravity acts equally on both objects because they are defined as having the same mass, the medium they fall through—air—introduces upward forces that counteract their descent. By applying Archimedes' Principle, you can see that because the piece of paper has a much larger volume and lower density than the coin, it displaces a greater volume of air, resulting in a significantly higher buoyant force pushing upward against it.

To arrive at Option B, your reasoning should focus on the net force acting on each object. Since the downward pull ($mg$) is identical for both, any difference in travel time must be caused by the upward resistive forces (buoyancy and air drag). The paper's expanded shape means the upward push from the air is more substantial, effectively reducing its net acceleration compared to the compact, dense coin. This transition from theoretical physics to a real-world scenario is a classic application of the Laws of Motion as detailed in NCERT Class 9 Science.

UPSC often includes "traps" like Option A to see if you will second-guess the data provided; if the masses are equal, the gravitational pull must be equal regardless of shape. Option D is another common distractor that describes the visual result (the fluttering, longer path) rather than the underlying physical cause. By systematically eliminating these based on the definitions of mass and force, you can confidently identify that the increased upward force on the paper is the primary reason for the delay, making Option B the only scientifically sound choice.