A body is lifted by a man to a height of 1 metre in 30 seconds. Another man lifts the same body to the same height in 60 seconds. The work done by them respectively are in the ratio of

1. Fundamental Mechanics: Force and Motion (basic)

Welcome to your first step in mastering mechanics! To understand how the world moves, we must start with the most fundamental concept: Force. In simple terms, a force is a push or a pull exerted on an object resulting from its interaction with another object Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.77. We measure force in a unit called the newton (N). Whether you are kicking a football or a magnet is pulling a nail, a force is being applied.

Forces are generally categorized into two types based on how they interact:

Type of Force	Description	Examples
Contact Forces	Require physical touch between objects.	Muscular force (lifting a box), Frictional force Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.77.
Non-contact Forces	Act through a space without physical touch.	Gravity, Magnetic force, Electrostatic force Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.77.

Now, let's look at the effects of force. A force doesn't just exist; it does things. It can make a stationary object move, change the speed of a moving object, change its direction, or even change its shape, like kneading dough or stretching a rubber band Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.65. When a force causes an object to move across a distance, we say Work has been done.

This brings us to a critical distinction in physics: Work vs. Time. Work done (W) is calculated as the product of the Force (F) applied and the Displacement (d) in the direction of that force: W = F × d. Notice that time is not part of this equation. If you lift a 10 kg weight to a height of 1 meter, the work you do depends only on the weight of the object and the height you reached. It doesn't matter if you lift it in 1 second or 100 seconds; the total work output remains exactly the same.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.77; Science, Class VIII. NCERT (Revised ed 2025), Exploring Forces, p.65

2. Gravitation and the Concept of Weight (basic)

At its heart, gravitation is the invisible force of attraction that exists between any two objects with mass. In our daily lives, we experience this primarily as the Earth's pull on us, which we call weight. While we often use 'mass' and 'weight' as synonyms in casual conversation, they represent two very different physical realities. Mass is the actual quantity of matter contained within an object and remains constant regardless of where you are in the universe. In contrast, weight is the gravitational force exerted on that mass Science Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.142. This relationship is expressed by the formula W = mg, where 'm' is mass and 'g' is the acceleration due to gravity.

Because weight depends on the strength of gravity (g), your weight changes depending on your location. For instance, the Sun’s gravity is a massive 274 m/s², which is about 28 times stronger than Earth's, whereas the Moon's gravity is only about 1.62 m/s² Physical Geography by PMF IAS, The Solar System, p.23. This means you would feel incredibly heavy on the Sun but light enough to leap great distances on the Moon, even though your actual body mass (the amount of 'you') hasn't changed at all.

Feature	Mass	Weight
Definition	Quantity of matter in an object.	Force of gravitational attraction.
SI Unit	Kilogram (kg).	Newton (N).
Variability	Constant everywhere.	Changes with gravity of the planet/location.

Even on Earth, gravity is not perfectly uniform. It is greater near the poles and less at the equator because the Earth is not a perfect sphere; the equator is further from the center of mass than the poles are Fundamentals of Physical Geography Class XI, The Origin and Evolution of the Earth, p.19. Beyond just keeping us grounded, gravity is the "engine" of our landscape. Without it, there would be no gradients, meaning water wouldn't flow downhill and geomorphic processes like erosion and transportation would simply stop Fundamentals of Physical Geography Class XI, Geomorphic Processes, p.38.

Sources: Science Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.142; Physical Geography by PMF IAS, The Solar System, p.23; Fundamentals of Physical Geography Class XI, The Origin and Evolution of the Earth, p.19; Fundamentals of Physical Geography Class XI, Geomorphic Processes, p.38

3. Mechanical Energy: Kinetic and Potential (intermediate)

In our journey through mechanics, we now encounter Mechanical Energy, which is the sum of an object's energy due to its motion and its position. Think of it as the "total capacity" an object has to perform work. It is divided into two primary forms: Kinetic Energy (KE), the energy of motion, and Potential Energy (PE), the stored energy of position. For instance, in our atmosphere, we observe that the kinetic energy of moving molecules is transmitted as sensible heat—the faster they move, the higher the temperature we sense Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.8. This energy is mathematically expressed as KE = ½mv², meaning it increases significantly with even a small increase in speed (velocity).

On the other hand, Gravitational Potential Energy is the energy an object possesses because of its height above the ground. When you lift a mass (m) to a height (h) against the pull of gravity (g), you do work on it, and that work is stored as potential energy: PE = mgh. It is important to remember that while we often treat gravity as a constant, it actually varies across the Earth's surface due to the uneven distribution of mass—a phenomenon known as a gravity anomaly Physical Geography by PMF IAS, Earths Interior, p.58. Therefore, the exact potential energy of an object can technically vary slightly depending on where on Earth you are standing!

A crucial distinction for your exams is the relationship between Work, Energy, and Power. Work is defined as force multiplied by displacement (W = F × d). When you lift an object, the work you do is exactly equal to the potential energy the object gains. Note that work depends only on the force and the distance, not on how fast you do it. Power, however, is the rate at which this work is done (P = Work / Time). If two people lift the same weight to the same height, they perform identical work and the weight gains the same potential energy, even if one person finishes the task faster than the other. The faster person simply generated more power Science , class X (NCERT 2025 ed.), Electricity, p.191.

Concept	Definition	Formula
Kinetic Energy	Energy due to motion.	KE = ½mv²
Potential Energy	Energy due to position/height.	PE = mgh
Power	Rate of doing work.	P = Work / Time

Sources: Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.8; Physical Geography by PMF IAS, Earths Interior, p.58; Science , class X (NCERT 2025 ed.), Electricity, p.191

4. Connected Concept: Conservation of Energy (intermediate)

In physics, the Law of Conservation of Energy states that energy can neither be created nor destroyed; it can only be transformed from one form to another. In the realm of basic mechanics, we see this in action through the Work-Energy Theorem. When you apply a force to move an object, you are doing Work (W), which is the product of the force applied and the displacement in the direction of that force (W = F × d).

Consider the act of lifting an object against gravity. To lift a mass (m), you must apply a force equal to its weight (mg). If you lift it to a height (h), the work done is W = mgh. This work doesn't disappear; it is stored as Gravitational Potential Energy. This principle of transformation is universal—for instance, wind turbines convert the kinetic energy of moving air into electrical energy INDIA PEOPLE AND ECONOMY, TEXTBOOK IN GEOGRAPHY FOR CLASS XII, Mineral and Energy Resources, p.61. While energy is conserved in a closed system, in real-world mechanical systems, some energy is often "lost" as heat due to friction, a process known as dissipation Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.14.

A crucial distinction for any UPSC aspirant is the difference between Work and Power. Work is strictly about the total energy transferred, regardless of time. Whether you lift a bag of grain in 2 seconds or 20 minutes, if the weight and the height are the same, the Work Done remains identical. However, the rate at which you do that work is called Power (Power = Work / Time). A more powerful machine doesn't necessarily do more work; it simply does the same work faster.

Concept	Definition	Formula	Key Characteristic
Work	Energy transferred by a force	W = F × d	Independent of time taken.
Power	Rate of doing work	P = W / t	Depends directly on time.

In the broader context of national development, Energy Conservation is not just a law of physics but a sustainable development strategy. Because our traditional fossil fuels are exhaustible, reducing consumption and increasing efficiency is imperative for economic survival Geography of India, Majid Husain, Energy Resources, p.31. Promoting conservation and renewable sources are the "twin planks" of a sustainable future for India Contemporary India II: Textbook in Geography for Class X, Print Culture and the Modern World, p.118.

Sources: INDIA PEOPLE AND ECONOMY, TEXTBOOK IN GEOGRAPHY FOR CLASS XII, Mineral and Energy Resources, p.61; Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.14; Geography of India, Majid Husain, Energy Resources, p.31; Contemporary India II: Textbook in Geography for Class X, Print Culture and the Modern World, p.118

5. Connected Concept: Friction and Resistance (intermediate)

When we think of movement, we often focus on the push or pull that starts it. However, in the real world, motion is rarely "free." There is almost always a hidden force working in the opposite direction, trying to slow things down or prevent them from moving in the first place. This force is friction.

At its core, friction is a contact force. This means it only comes into play when two surfaces are physically touching Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.68. Even surfaces that look perfectly smooth to the naked eye—like a polished marble floor or a sheet of glass—are actually jagged and mountain-like at a microscopic level. When these two surfaces meet, their irregularities lock into each other. To move one object over another, you must apply enough force to overcome this microscopic interlocking.

The strength of this resistance depends heavily on the nature of the surfaces in contact. Friction is significantly greater on rough surfaces because the irregularities are deeper and lock more firmly. Conversely, friction is minimal on smooth surfaces or over liquids, such as the sea surface Physical Geography by PMF IAS, Pressure Systems and Wind System, p.307. To understand the variety of forces we encounter, consider this comparison:

Type of Force	Description	Examples
Contact Force	Requires physical touch to exert influence.	Friction, Muscular Force
Non-Contact Force	Acts over a distance without physical touch.	Magnetic, Gravitational, Electrostatic

Friction isn't just a concept for sliding blocks in a lab; it shapes our entire planet. In Geography, we see friction resisting the movement of wind. Near the Earth's surface, the friction caused by landforms (trees, mountains, buildings) slows down the wind and even changes its direction. This influence typically extends up to 1-3 km into the atmosphere Physical Geography by PMF IAS, Pressure Systems and Wind System, p.307. Without friction, we wouldn't be able to walk (our shoes would just slide), and cars wouldn't be able to brake!

Sources: Science, Class VIII, NCERT (Revised ed 2025), Exploring Forces, p.68, 70, 77; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.307

6. Defining Work Done in Physics (intermediate)

In physics, Work Done has a very specific meaning that differs from our everyday usage of the word. We might say a student studying for hours is 'doing a lot of work,' but in mechanics, work is strictly defined as the product of the force applied and the displacement caused in the direction of that force. The formula is expressed as W = F × d. If you push against a wall with all your might but the wall doesn't move, the displacement is zero, and therefore, scientifically speaking, you have done zero work on the wall. The SI unit of work is the Joule (J), which is defined as the work done when a force of one Newton moves an object through a distance of one metre Science, Class X, Electricity, p.173.

When we lift an object vertically, the force we must apply is equal to the object's weight (which is its mass multiplied by gravity, or mg). Therefore, the work done to lift a body to a certain height (h) is calculated as W = mgh. A critical point to master is that work is independent of time. Whether you lift a heavy box to a shelf in two seconds or two minutes, the total work performed is identical because the force required and the distance moved remain the same. While the rate at which you do work (known as Power) changes with time, the total energy transferred—the work itself—does not.

Factor	Impact on Work Done	Reasoning
Force (F)	Directly Proportional	More force over the same distance equals more work.
Displacement (d)	Directly Proportional	The further the object moves, the more work is done.
Time (t)	No Impact	Work only cares about the 'start' and 'end' state, not the speed.

Sources: Science, Class X, Electricity, p.173

7. Power: The Rate of Doing Work (exam-level)

When we discuss Work, we are focusing on the total energy transferred to an object, calculated as the product of force and displacement (W = F × d). However, in mechanics and engineering, we often need to know not just how much work was done, but how fast it was accomplished. This "time rate" of doing work is what we define as Power.

Mathematically, if an agent does an amount of work W in time t, then the average power is given by the formula: Power (P) = Work (W) / Time (t). This relationship highlights a crucial distinction: while Work is independent of time, Power is inversely proportional to it. This means if two people perform the exact same task—such as lifting a specific weight to a specific height—they perform the same amount of work, regardless of who finishes first. However, the person who completes the task in less time is said to have exerted more power Science, class X (NCERT 2025 ed.), Electricity, p.188.

The SI unit of power is the Watt (W), named after James Watt. One Watt is defined as the power of an agent which does work at the rate of 1 Joule per second. We can also see this concept reflected in electrical circuits, where power is the rate at which electrical energy is consumed or transferred Science, class X (NCERT 2025 ed.), Electricity, p.173. In the context of lifting bodies, the work done is equivalent to the change in potential energy (mgh); therefore, the power exerted is (mgh)/t.

Concept	Definition	Depends on Time?
Work	Total energy transferred (Force × Displacement)	No
Power	The rate at which work is done (Work / Time)	Yes

Sources: Science, class X (NCERT 2025 ed.), Electricity, p.188; Science, class X (NCERT 2025 ed.), Electricity, p.173

8. Solving the Original PYQ (exam-level)

In this problem, we see the perfect application of the fundamental definition of Work Done. You've learned that work is calculated as the product of Force and Displacement in the direction of that force (W = F × s). When lifting an object against gravity, the force required is exactly equal to its weight (mg). Since both men are lifting the same body to the same height, the variables for mass, gravity, and distance remain identical for both individuals. According to the principles found in NCERT Class 9 Science (Chapter: Work and Energy), work is a scalar quantity that depends solely on the magnitude of the force and the displacement, regardless of the time elapsed.

To arrive at the correct answer, you must mentally separate the outcome from the duration. Man A performs work equal to mg × 1, and Man B performs work equal to mg × 1. Because the time component (30 seconds vs. 60 seconds) does not enter the formula for work, it is a "distractor" variable that should be ignored for this specific calculation. Since the numerators and denominators in our ratio are equal, the work done by both men is exactly the same, resulting in a ratio of 1 : 1. This makes Option (B) the only logically sound choice.

The primary trap UPSC has set here is the confusion between Work and Power. Options (A) and (C) are designed to catch students who mistakenly apply the time variable. Power is defined as the rate of doing work (P = W/t). While the first man is indeed more "powerful" because he completes the task faster (generating a 2:1 power ratio), the total Work Done—the energy required to move that specific mass to that specific height—remains constant. Always remember: Work is about the 'how much,' while Power is about the 'how fast.'