Which one of the following statements for second law of motion is NOT correct ?

1. Basics of Motion: Velocity and Acceleration (basic)

To master mechanics, we must first distinguish between how fast something moves and where it is headed. Speed is a simple measure of distance covered over time, but in the UPSC syllabus, we focus more on Velocity. Velocity is a vector quantity, meaning it includes both magnitude (speed) and direction. For example, a train moving at 100 km/h is its speed, but 100 km/h due North is its velocity. If the train rounds a curve even at a steady speed, its velocity changes because its direction is changing.

This brings us to the core concept of Acceleration, which is defined as the rate of change of velocity over time. It is not simply "moving fast," but rather how quickly the velocity is increasing, decreasing, or changing direction. Mathematically, it is expressed as:
a = (v - u) / t
where 'v' is the final velocity, 'u' is the initial velocity, and 't' is the time taken. If an object maintains a constant velocity in a straight line, its acceleration is zero, a state known as uniform linear motion Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.117.

In the real world, non-uniform motion is far more common Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.119. Whether it is a car braking for a signal or a planet orbiting the sun, the velocity is constantly fluctuating. It is essential to understand that Force is the driver of this change. According to Newton’s Second Law, the net force acting on a body is proportional to the rate of change of its momentum. For an object with a constant mass, this simplifies to the relationship F = ma, meaning force is directly proportional to acceleration. Thus, acceleration always occurs in the same direction as the net force applied.

Sources: Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.117; Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.119

2. Newton's First Law and the Concept of Inertia (basic)

Hello! Now that we have a basic understanding of what a force is — essentially a push or a pull as described in Science ,Class VIII . NCERT, Exploring Forces, p.77 — let’s dive into how objects naturally behave when forces are or are not acting on them. This brings us to Newton’s First Law of Motion, often called the Law of Inertia.

Think of Inertia as the inherent "laziness" of matter. Every object has a natural tendency to resist any change in its state of motion. If an object is at rest, it wants to stay at rest. If it is moving in a straight line at a steady speed, it wants to keep moving exactly that way. Newton’s First Law formalizes this by stating: An object will remain at rest or continue to move at a constant velocity unless acted upon by an external, unbalanced force. This is why a train, as noted in Science-Class VII . NCERT, Measurement of Time and Motion, p.116, requires an engine's force to start moving from a station and brakes to eventually slow down and stop.

It is important to understand that Mass is the quantitative measure of inertia. The more mass an object has, the greater its inertia, and the harder it is to change its state of motion. For example, it is much easier to push a bicycle than a stalled car because the car has more mass and, therefore, more inertia. This principle was heavily influenced by the early investigations of Galileo Galilei, who realized through his experiments with pendulums and inclined planes that motion does not simply "run out" on its own; rather, external forces like friction are what usually bring things to a halt Science-Class VII . NCERT, Measurement of Time and Motion, p.108.

In the UPSC context, remember that Newton's First Law defines Force qualitatively: it is the "agent" that overcomes inertia. Without a net force, an object’s velocity (both its speed and its direction) remains constant.

Sources: Science ,Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.77; Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.108, 116

3. Linear Momentum: The 'Quantity' of Motion (intermediate)

In our journey through mechanics, we often talk about how fast things move, but linear momentum introduces a deeper layer: the physical 'impact' or 'quantity' of that motion. Imagine a bicycle and a heavy truck both moving toward you at 5 m/s. Even though their speeds are identical, the truck is significantly harder to stop. This is because momentum depends not just on how fast an object is going, but also on how much 'stuff' (mass) is moving. When an object moves along a straight line, it is in linear motion Science-Class VII, Measurement of Time and Motion, p.116, and its linear momentum (p) is defined as the product of its mass (m) and its velocity (v): p = mv.

It is crucial to remember that momentum is a vector quantity. This means it has both a magnitude and a specific direction, which is always the same as the direction of the object's velocity. If the speed of an object changes—what we call non-uniform linear motion Science-Class VII, Measurement of Time and Motion, p.117—its momentum also changes. The units we use reflect this relationship: since mass is measured in kilograms (kg) and velocity in metres per second (m/s) Science-Class VII, Measurement of Time and Motion, p.113, the SI unit for momentum is kg·m/s.

The real magic happens when we apply a Force. According to Newton’s Second Law, the net force acting on a body is not proportional to the momentum itself, but to the rate of change of momentum over time (F = dp/dt). If the mass of the object stays constant, this relationship simplifies to the famous F = ma (Force = mass × acceleration). This tells us that a force is required to change an object's momentum, whether that means speeding it up, slowing it down, or changing its direction.

Feature	Mass (m)	Velocity (v)	Momentum (p)
Type	Scalar (Magnitude only)	Vector (Mag + Direction)	Vector (Mag + Direction)
Role	Inertia/Amount of matter	Rate of displacement	"Quantity" of motion

Sources: Science-Class VII, Measurement of Time and Motion, p.116; Science-Class VII, Measurement of Time and Motion, p.117; Science-Class VII, Measurement of Time and Motion, p.113; Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.141

4. Conservation of Linear Momentum (intermediate)

To understand the Conservation of Linear Momentum, we must first recall what momentum is: the 'quantity of motion' an object possesses, calculated as the product of its mass and velocity (p = mv). In our previous discussions, we established that a force is essential to change the speed or direction of an object Science, Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.67. Newton’s Second Law takes this further, stating that the net force acting on an object is equal to the rate of change of its momentum (F = dp/dt). This means that if no external force acts on a system, the momentum cannot change.

The Law of Conservation of Momentum states that the total momentum of an isolated system (a system with no external forces) remains constant over time. Think of a mid-air collision between two billiard balls. While ball A exerts a force on ball B, and ball B exerts an equal and opposite force on ball A (Newton's Third Law), these are internal forces. Because there is no net external force acting on the pair of balls together, the sum of their momenta before the crash must exactly equal the sum of their momenta after the crash. Even when objects change their individual speeds or directions, the system as a whole preserves its total 'quantity of motion'.

This principle is a pillar of physics because it applies everywhere—from the subatomic level to the movement of galaxies. For example, when a rifle is fired, the forward momentum of the bullet is exactly balanced by the backward 'recoil' momentum of the rifle. Since the rifle is much heavier than the bullet, it moves backward at a much lower speed, but the total momentum of the rifle-bullet system remains zero (just as it was before the trigger was pulled).

Sources: Science, Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.67; Science, Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.64

5. Newton's Third Law: Action and Reaction (basic)

Newton’s Third Law of Motion describes the fundamental nature of forces as interactions between two entities. It states: “To every action, there is always an equal and opposite reaction.” While we often use the word 'action' and 'reaction' in biology to describe a delayed response to a stimulus—like a reflex action Science, Class X, Control and Coordination, p.102—in physics, these forces are perfectly simultaneous. There is no time delay between the action and the reaction.

The most crucial concept to grasp for competitive exams is that action and reaction always act on two different bodies. Even though they are equal in magnitude and opposite in direction, they do not cancel each other out because they are applied to different objects. For example, a force is essentially a push or pull resulting from an object's interaction with another Science, Class VIII, Exploring Forces, p.77. When you sit on a chair, your body exerts a downward force on the chair (Action), and the chair exerts an upward force on your body (Reaction).

Feature	Action Force	Reaction Force
Magnitude	Equal to Reaction	Equal to Action
Direction	Opposite to Reaction	Opposite to Action
Point of Application	Object A	Object B
Timing	Instantaneous	Instantaneous

Think of propulsion: A swimmer pushes the water backward (Action), and the water pushes the swimmer forward (Reaction). Similarly, in a rocket, the accelerating exhaust gases are pushed downward, and those gases exert an equal upward force on the rocket, allowing it to overcome gravity and move upward. In both cases, motion occurs because the reaction force acts on the person or the vehicle, not on the medium being pushed.

Sources: Science, Class VIII, Exploring Forces, p.77; Science, Class X, Control and Coordination, p.102

6. Work, Energy, and Power Relations (intermediate)

In the realm of mechanics, Work, Energy, and Power form an interconnected trinity that describes how forces interact with objects over time and space. To understand them, we must look at them as a process of exchange. Work is the act of transferring energy; it occurs when a force acts upon an object to cause a displacement (W = F × d). If you push against a wall and it doesn’t move, scientifically speaking, you have done zero work, regardless of how much you sweat. Energy is the 'currency' required to perform this work—the capacity to make things happen. It exists in various forms, such as kinetic energy (the energy of motion) or potential energy (stored energy).

The bridge between these two is the Work-Energy Theorem, which states that the net work done on an object is exactly equal to the change in its kinetic energy. In biological systems, this is visible when the food we eat acts as fuel, providing the chemical energy necessary for our bodies to perform mechanical work Science, Class X (NCERT 2025 ed.), Our Environment, p.210. However, the transformation of energy is never perfectly efficient. When work is performed, some energy is inevitably dissipated, usually as heat, which increases the vibrational energy (temperature) of the surroundings Environment and Ecology, Majid Hussain (Access publishing 3rd ed.), BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.8, 14. This dissipation is why energy flow in an ecosystem is unidirectional—it moves from producers to consumers but cannot be fully recycled back Environment, Shankar IAS Academy (ed 10th), Functions of an Ecosystem, p.11.

Finally, Power adds the dimension of time to this relationship. It is defined as the rate at which work is done or energy is transferred (P = W/t). Two engines might do the same amount of work (lifting a weight), but the more powerful engine will do it faster. Understanding these relations is crucial because it explains why energy is the basic force responsible for all metabolic and mechanical activities in our world.

Concept	Definition	Standard Unit
Work	Energy transfer via force and displacement (W = F × d cosθ)	Joule (J)
Energy	The capacity or ability to do work (e.g., ½mv²)	Joule (J)
Power	The speed or rate at which work is performed (P = W/t)	Watt (W)

Sources: Science, Class X (NCERT 2025 ed.), Our Environment, p.210; Environment and Ecology, Majid Hussain (Access publishing 3rd ed.), BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.8, 14; Environment, Shankar IAS Academy (ed 10th), Functions of an Ecosystem, p.11

7. Newton's Second Law: Force and Rate of Change (exam-level)

Newton’s Second Law of Motion provides the mathematical link between the forces acting on an object and the resulting change in its motion. While the First Law defines force qualitatively (as something that overcomes inertia), the Second Law quantifies it. It states that the net force acting on a body is directly proportional to the rate of change of its momentum over time. It is crucial to distinguish between momentum and the change in momentum: an object can have massive momentum (like a heavy train moving at constant speed), but if that momentum isn't changing, the net force acting on it is zero.

Mathematically, momentum (p) is the product of mass and velocity (p = mv). The law is expressed as F = dp/dt. In most scenarios where the mass of the object remains constant, this relationship simplifies to the famous formula F = ma (Force = mass × acceleration). This tells us that to produce a specific acceleration, the force required is proportional to the object's mass. Furthermore, both force and acceleration are vector quantities, meaning they have both magnitude and direction. A key dictate of this law is that the acceleration produced is always in the exact same direction as the applied net force.

The standard SI unit for force is the newton (N) Science, Class VIII, Exploring Forces, p.65. Understanding this law also helps us understand weight, which is not just a value on a scale but the specific gravitational force with which the Earth pulls an object toward its center Science, Class VIII, Exploring Forces, p.72. Because weight is a force, it is also measured in newtons (N).

Sources: Science, Class VIII, Exploring Forces, p.65; Science, Class VIII, Exploring Forces, p.72

8. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamental building blocks of Newton’s Laws of Motion, this question serves as a perfect test of your conceptual precision. The core principle you learned is that force is not merely related to movement, but specifically to the change in movement. In the UPSC examination, the examiners often test whether you can distinguish between a physical quantity and its time rate of change. The Second Law is mathematically defined as F = dp/dt, which means the net force is equivalent to how quickly momentum varies over time, not the absolute value of the momentum itself.

To arrive at the correct answer, you must evaluate each statement against the formula F = ma (for constant mass). Statement (C) is the formal definition of the law, while statements (A) and (B) are the direct consequences of that definition: because force and acceleration are vector quantities, they must share the same direction, and their magnitudes remain proportional. However, Statement (D) fails because it suggests that a body with high momentum (like a heavy truck cruising at a constant velocity) must have a high net force acting on it. In reality, if the momentum is not changing, the net force is zero, regardless of how large the momentum is.

The trap here lies in the subtle phrasing of Option (D). UPSC frequently uses "distractor" options that sound scientifically plausible but swap a rate for a static value. While force influences momentum, it is only proportional to the rate of change. This is why Statement (D) is NOT correct and is the required answer. Always remember: force is the agent of change, not a measure of the current state of motion. NASA Glenn Research Center