A girl is swinging on a swing in sitting position. When the same girl stands up, the period of swing will

1. Types of Motion: Periodic and Oscillatory (basic)

Welcome to your first step in mastering mechanics! To understand how the world moves, we must first distinguish between motion that happens once and motion that repeats itself. Periodic Motion is any movement that repeats itself at regular intervals of time. Think of the hands of a clock or the Earth revolving around the Sun; these movements are predictable because they follow a strict schedule. Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p.109

A specific and fascinating sub-type of periodic motion is Oscillatory Motion. This is the "to-and-fro" or "back-and-forth" movement of an object about a central point, known as its mean position. A classic example is a simple pendulum, which consists of a small metallic ball (called a bob) suspended by a string. When you pull the bob to one side and release it, it oscillates. It passes through the center, reaches the other side, and comes back again. This complete round trip is called one oscillation. Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p.109

The most critical measurement in this context is the Time Period—the exact time taken by the pendulum to complete one full oscillation. Interestingly, for a pendulum of a fixed length at a specific location, this time period remains constant. Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p.118 To help you distinguish these concepts, remember this rule of thumb:

Feature	Periodic Motion	Oscillatory Motion
Core Nature	Repeats at fixed intervals.	Moves back and forth about a center.
Example	The Moon orbiting the Earth.	A child on a playground swing.
Relationship	A broad category.	A specific type of periodic motion.

Sources: Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p.109; Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p.118

2. Acceleration due to Gravity (g) (basic)

To understand acceleration due to gravity (g), we must first recognize gravity as the fundamental force that keeps us anchored to the surface. It acts as a "switch" that triggers the movement of all surface materials, from a falling fruit to the massive flow of glaciers Science, Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.77. When an object falls freely toward the Earth, its velocity increases every second; this rate of increase is what we call g.

On Earth, the average value of g is approximately 9.8 m/s². However, this value is not uniform across the globe. Because the Earth is an oblate spheroid (bulging at the equator and flattened at the poles), the distance from the center to the surface is greater at the equator than at the poles. Since gravity weakens as distance increases, the value of g is greater near the poles and less at the equator FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19.

Furthermore, g is influenced by the mass of the planet and the distribution of material within its crust. For instance, the Sun, being immensely massive, has a surface gravity 28 times that of Earth, while the Moon’s gravity is much weaker Physical Geography by PMF IAS, Manjunath Thamminidi, The Solar System, p.23. Even on Earth, uneven mass distribution leads to "gravity anomalies," where the measured gravity differs from the expected value, providing scientists with clues about the materials hidden beneath the crust.

Celestial Body	Surface Gravity (g)	Comparison to Earth
Sun	274 m/s²	~28 times Earth
Earth	9.8 m/s²	Standard (1g)
Moon	1.62 m/s²	~1/6th of Earth

Sources: Science, Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.77; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19; Physical Geography by PMF IAS, The Solar System, p.23

3. Basics of Simple Harmonic Motion (SHM) (intermediate)

At its heart, Simple Harmonic Motion (SHM) is a type of periodic motion where an object moves back and forth about a central point, known as the mean position. A classic example we see in everyday life is the simple pendulum. As described in Science-Class VII, Measurement of Time and Motion, p.109, a pendulum consists of a small mass (the bob) suspended by a string. When you pull it to one side and release it, a 'restoring force' (gravity) pulls it back toward the center, causing it to oscillate. This motion is periodic because it repeats itself at regular intervals of time.

The most critical concept to master here is the Time Period (T), which is the time taken to complete one full oscillation (Science-Class VII, Measurement of Time and Motion, p.118). For a simple pendulum, this period is determined by a specific mathematical relationship: T = 2π√(L/g). Here, L represents the effective length of the pendulum and g is the acceleration due to gravity. Interestingly, the mass of the bob does not appear in this formula, meaning a heavy bob and a light bob will take the same time to swing if their strings are the same length.

However, the effective length (L) is not just the length of the string; it is the distance from the pivot point to the Center of Mass of the oscillating system. This is a vital distinction. If the distribution of mass changes—for instance, if a person on a swing stands up—the center of mass shifts upward, closer to the pivot. This effectively shortens the length (L). According to our formula, if L decreases, the Time Period (T) also decreases, meaning the pendulum swings faster. This principle explains why the 'rhythm' of a swing changes based on the rider's posture.

Sources: Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.109; Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.118

4. Conservation of Mechanical Energy (intermediate)

Mechanical energy is the total energy possessed by an object due to its motion and its position. It is calculated as the sum of Kinetic Energy (KE)—the energy of motion—and Potential Energy (PE)—the energy stored due to an object's position or configuration. The Law of Conservation of Mechanical Energy states that in an isolated system where only conservative forces (like gravity) are acting, the total mechanical energy remains constant. In other words, energy is neither created nor destroyed; it merely transforms from one form to another.

Consider a child on a playground swing. A swing functions as a simple pendulum Science-Class VII . NCERT, Measurement of Time and Motion, p.119. At the highest point of the swing's path, the child momentarily stops, meaning KE is zero and PE is at its maximum. As the swing descends, gravity pulls it downward, converting that PE into KE. At the lowest point of the arc, the swing reaches its maximum speed (maximum KE) while its PE is at its minimum. This continuous exchange between KE and PE keeps the system in motion.

An intermediate application of this concept involves changing the system's Center of Mass (CoM). The time period (T) of a pendulum—the time it takes to complete one full back-and-forth swing—is determined by the formula T = 2π√(L/g), where L is the effective length from the pivot to the CoM. If a person stands up while swinging, their body's center of mass moves upward toward the pivot point. This action reduces the effective length (L) of the pendulum. Since the period T is directly proportional to the square root of L, a decrease in length leads to a shorter time period, making the swing oscillate faster.

In broader engineering, we see these principles applied to energy harvesting. For example, wind turbines are designed to capture the kinetic energy of moving air and convert it into mechanical energy through the rotation of blades Environment, Shankar IAS Academy, Renewable Energy, p.290. Whether in a simple playground swing or a massive industrial turbine, the transformation and conservation of mechanical energy are the governing rules of motion.

Sources: Science-Class VII . NCERT, Measurement of Time and Motion, p.119; Environment, Shankar IAS Academy, Renewable Energy, p.290

5. Circular Motion and Centripetal Force (intermediate)

In our previous hops, we looked at how objects move in a straight line, which we call linear motion Science-Class VII, Measurement of Time and Motion, p.116. However, when an object moves along a curved path, we enter the realm of circular motion. Unlike linear motion where an object can move at a constant velocity, an object in circular motion is always accelerating. Why? Because velocity is a vector—even if the speed stays the same, the direction is constantly changing. To create this change in direction, a force must act toward the center of the circle; we call this the centripetal force. In nature, this force is everywhere. For instance, in meteorology, centripetal acceleration acts on air flowing around centers of circulation, creating the circular patterns (vortices) we see in cyclones and anticyclones Physical Geography by PMF IAS, Pressure Systems and Wind System, p.309. From a perspective inside the rotating system, one might also feel an outward 'pull' known as centrifugal force. This is why the Earth has an equatorial bulge; the speed of rotation is higher at the equator, leading to a greater centrifugal force that counteracts gravity slightly more there than at the poles Physical Geography by PMF IAS, Latitudes and Longitudes, p.241. A fascinating application of these principles is a playground swing, which moves in a circular arc. The time it takes to complete one swing (the period) depends on the effective length of the pendulum—the distance from the pivot to the system's centre of mass. When a person stands up on a swing, they raise their body's center of mass toward the pivot. This effectively shortens the length (L) of the pendulum. Because the period is calculated as T = 2π√(L/g), a shorter length leads to a shorter time period, making the swing oscillate faster.

Concept	Direction of Force	Daily Life Example
Centripetal Force	Inward (Center-seeking)	String pulling a stone in a circle; Gravity on a satellite.
Centrifugal Force	Outward (Apparent)	Passengers leaning outward when a car turns sharply.

Sources: Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.116; Physical Geography by PMF IAS, Latitudes and Longitudes, p.241; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.309

6. Concept of Centre of Mass and Centre of Gravity (intermediate)

To understand mechanics, we must first master the concept of the Centre of Mass (CoM). Think of the CoM as the 'average' location of all the mass in an object. It is the specific point where the entire mass of the body can be assumed to be concentrated for the purpose of describing its motion. For a uniform, symmetrical object like a sphere, the CoM is right at its geometric centre. However, for irregular objects, the CoM shifts toward the heavier side. This is why the Earth's density variations create 'gravity anomalies' — the uneven distribution of mass within the crust changes how gravity pulls on objects at the surface FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19. While the CoM deals with mass, the Centre of Gravity (CoG) is the point through which the force of gravity (weight) acts on an object. In most everyday scenarios, the CoM and CoG are at the exact same point. However, they can differ if the object is so large that the strength of gravity changes from one part of the object to another. For example, because the Earth is an oblate spheroid (bulging at the equator), you are actually closer to the Earth's CoM when you are at the poles, resulting in a stronger gravitational pull there Physical Geography by PMF IAS, Latitudes and Longitudes, p.241.

Feature	Centre of Mass (CoM)	Centre of Gravity (CoG)
Definition	The point where the mass of the object is balanced.	The point where the weight (force of gravity) is balanced.
Dependent on	Distribution of matter/mass.	Distribution of mass AND the external gravitational field.
Practical context	Determines how an object moves when pushed.	Determines the stability and balance of an object.

One of the most fascinating applications of this concept is seen in pendulum motion. The time period (T) of a pendulum (like a swing) depends on its 'effective length' (L), which is the distance from the pivot to the CoM of the system. If you change your posture—for example, by standing up on a swing—you are physically moving your mass upward. This raises the system's CoM, effectively shortening the length of the pendulum. According to the formula T = 2π√(L/g), a shorter length leads to a shorter time period, meaning the swing oscillates faster Science, Class VIII, Exploring Forces, p.72.

Sources: FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), The Origin and Evolution of the Earth, p.19; Physical Geography by PMF IAS, Latitudes and Longitudes, p.241; Science, Class VIII. NCERT(Revised ed 2025), Exploring Forces, p.72

7. Factors Affecting Pendulum Time Period (exam-level)

To understand how a pendulum behaves, we first define the Time Period: the time taken to complete one full oscillation (moving from the center to one side, then the other, and back to center) Science-Class VII . NCERT(Revised ed 2025), Chapter 8, p.109. While it might seem intuitive that a heavier object would swing faster, physics reveals that the time period of a simple pendulum is actually independent of its mass. Whether you use a heavy metal bob or a light wooden one, if the length of the string remains the same, the time period remains constant Science-Class VII . NCERT(Revised ed 2025), Chapter 8, p.110.

The core relationship is expressed by the formula T = 2π√(L/g). In this equation, T is the time period, L is the effective length, and g is the acceleration due to gravity. Because T is directly proportional to the square root of L, increasing the length of the pendulum will increase the time it takes to complete a swing, making it move more slowly. Conversely, shortening the length makes the pendulum swing faster.

A vital concept for competitive exams is the effective length. This is the distance from the pivot point to the Center of Mass of the swinging object. This explains why a person standing on a swing moves faster than when they are sitting. By standing up, the person raises their center of mass closer to the pivot, effectively decreasing the length (L) of the system. As L decreases, the time period T decreases, causing the swing to oscillate more rapidly.

Below is a summary of how different factors influence the pendulum's motion:

Factor	Change	Effect on Time Period (T)
Length (L)	Increase	Increases (Slower oscillations)
Mass (m)	Increase/Decrease	No Change
Gravity (g)	Decrease (e.g., on the Moon)	Increases (Slower oscillations)

Sources: Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p.109; Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p.110; Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p.118

8. Solving the Original PYQ (exam-level)

This question perfectly synthesizes two core physics concepts you've just mastered: the Simple Pendulum and the Center of Mass. As an aspirant, you must visualize the playground swing not just as an object, but as a physical pendulum where the effective length (L) is the distance from the pivot point to the girl's center of mass. By standing up, the girl is essentially "reconfiguring" the system's geometry. According to the fundamental formula T = 2π√(L/g), discussed in Science-Class VII . NCERT(Revised ed 2025), the time period is governed by this length and gravity, independent of the rider's total mass.

When the girl transitions from a sitting to a standing position, her body's center of mass moves upward, closer to the pivot. This physical shift effectively shortens the pendulum's length (L). Since the time period (T) is directly proportional to the square root of length, a decrease in L must result in a mathematical decrease in T. Therefore, the swing will complete its cycle more quickly, meaning the period will (A) be shorter. Reasoning cue: always ask yourself how a change in posture affects the distribution of mass relative to the point of rotation!

UPSC often includes distractors to test the depth of your conceptual clarity. Option (D) "not change" is a classic trap for students who correctly remember that mass does not affect the period but fail to account for the change in effective length. Option (C) "depend on the height of the girl" is a "half-truth" distractor; while her height influences how much the center of mass shifts, the qualitative result of standing up is always a shorter period regardless of her specific height. By focusing on the functional relationship between length and time, you can navigate these common traps with ease.