Gravitation Class 11 Physics Problems with Solutions | Complete Guide 2025-26

Struggling with gravitation physics problems? You’re not alone. This comprehensive guide helps physics students, AP Physics learners, and anyone preparing for competitive exams master the challenging world of gravitational concepts and calculations.

Who This Guide Is For:

• High school physics students tackling gravity problems for the first time

• AP Physics students preparing for exams

• College students reviewing fundamental concepts

• Anyone studying for competitive physics exams like JEE or NEET

Gravitation problems can feel overwhelming, but they follow predictable patterns once you understand the core principles. We’ll break down complex concepts into manageable steps, showing you how to tackle everything from basic Newton’s law of universal gravitation problems to advanced satellite orbital mechanics.

What You’ll Learn:
You’ll master Newton’s Law of Universal Gravitation and Core Principles, including how to calculate gravitational forces between objects and understand when and why the law applies. We’ll also dive deep into Satellite Mechanics and Orbital Dynamics, covering orbital velocity calculations, geostationary satellites, and the physics behind how objects stay in orbit. Finally, you’ll conquer Escape Velocity and Interplanetary Motion, learning how to determine the minimum speed needed for objects to break free from gravitational fields.

Each section includes step-by-step problem solutions, common mistakes to avoid, and practice problems that mirror what you’ll see on exams. By the end, you’ll approach gravitational field problems with confidence and tackle even the trickiest acceleration due to gravity calculations.

Newton’s Law of Universal Gravitation and Core Principles

Newton’s law of universal gravitation forms the cornerstone of gravitation physics problems, establishing that gravitational force is an attractive force between two masses m₁ and m₂ separated by a distance r. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, expressed mathematically as F = Gm₁m₂/r².

The universal gravitational constant G plays a crucial role in these calculations, with its precisely measured value of 6.67 × 10⁻¹¹ Nm²kg⁻². This constant remains uniform throughout the universe and is independent of the nature or size of bodies involved, as well as the medium between them. The dimensional formula for G is [M⁻¹L³T⁻²], which proves essential when solving gravitation physics problems involving dimensional analysis.

An important principle to remember when applying Newton’s law of universal gravitation is that while it technically applies to point masses, spherical bodies can be treated as if their entire mass is concentrated at the center of mass when calculating forces on external points. This simplification makes satellite orbital mechanics and planetary motion problems more manageable.

Key Properties of Gravitational Forces: Gravitation Class 11 Physics Problems with Solutions

Gravitational forces exhibit several distinctive characteristics that are fundamental to understanding gravitation physics problems. The force is both central, meaning it acts along the line joining the centers of the two masses, and conservative, allowing for the definition of gravitational potential energy in physics problems.

Despite its universal nature, gravitational force is remarkably weak compared to other fundamental forces. It measures approximately 10³⁶ times smaller than electrostatic force and 10¹⁸ times smaller than nuclear force, making it the weakest force in nature. However, this weakness is compensated by its unlimited range and its ability to act on all bodies regardless of their size, shape, or position.

The gravitational force between celestial bodies, such as the sun and planets, provides the necessary centripetal force for orbital motion, making it essential for solving satellite orbital mechanics problems. Newton’s third law of motion applies perfectly to gravitational interactions, creating action-reaction pairs between any two gravitating bodies. Additionally, gravitational force remains independent of the medium between particles, distinguishing it from other fundamental forces.

Important Limitations and Applications of Newton’s Law: Gravitation Class 11 Numericals with Solutions

While Newton’s law of universal gravitation proves highly effective for most gravitation physics problems, it does have specific limitations that must be acknowledged. The law holds accurately for both very large distances, such as those encountered in planetary motion problems, and relatively short distances in everyday scenarios.

However, Newton’s law fails when the distance between objects becomes less than 10⁻⁹ meters, which corresponds to intermolecular distances. At these scales, other forces become dominant, and quantum mechanical effects must be considered instead of classical gravitational theory.

The most common application of Newton’s law involves Earth’s gravitational pull, which we simply refer to as gravity. This application forms the basis for calculating acceleration due to gravity and solving numerous terrestrial gravitation physics problems. The law’s versatility extends to escape velocity calculations, where it determines the minimum speed needed for objects to overcome Earth’s gravitational field, and Kepler’s laws physics applications, where it explains the mathematical relationships governing planetary orbits and satellite mechanics.

Acceleration Due to Gravity and Its Variations: Gravitation Class 11 Physics Problems with Solutions

Acceleration due to gravity (g) represents the uniform acceleration experienced by any freely falling object under Earth’s gravitational influence. This fundamental concept in gravitation physics problems is a vector quantity measured in m/s², consistently directed toward Earth’s center regardless of the falling object’s mass.

For practical calculations, g maintains an approximate value of 9.8 m/s² at Earth’s surface, though this value exhibits slight variations depending on geographical location. This independence from object mass makes acceleration due to gravity a unique characteristic that simplifies many physics gravitation examples.

The mathematical relationship governing g follows the formula:
g = GM/R²

Where:

• G represents the gravitational constant

• M equals Earth’s mass (6.0 × 10²⁴ kg)

• R equals Earth’s radius (6.38 × 10⁶ m)

To understand the relative scale of gravitational acceleration, consider these comparative values:

• Moon’s surface: approximately one-sixth of Earth’s g

• Sun’s surface: roughly 27 times Earth’s g

• Mercury: exhibits the minimum acceleration due to gravity among all planets

Effects of Earth’s Shape and Rotation on Gravity: Gravitation Class 11 Physics Problems with Solutions

Now that we have covered the basic calculation of g, let’s examine how Earth’s physical characteristics influence gravitational acceleration. Earth’s elliptical shape creates significant variations in g across different latitudes, with minimum values occurring at the equator and maximum values at the poles.

This variation occurs because g maintains an inverse relationship with R², and Earth’s diameter measures smaller at the poles compared to the equatorial region. The mathematical expression accounting for rotational effects becomes:

g’ = g – Rω²cos²λ

Where:

• ω represents Earth’s angular velocity

• λ indicates the latitude

At the poles (λ = 90°), Earth’s rotation produces no effect on gravitational acceleration, maintaining g’ = g. Conversely, at the equator (λ = 0°), g reaches its minimum value where g’ = g – Rω².

If Earth hypothetically ceased rotating, gravitational acceleration would remain unchanged at the poles but would increase by Rω² at the equatorial regions.

How Altitude and Depth Affect Gravitational Acceleration

With this understanding of surface variations, let’s explore how distance from Earth’s center affects gravitational acceleration. Both altitude above and depth below Earth’s surface create measurable changes in g values.

For objects at height h above Earth’s surface, the gravitational acceleration follows:
g’ = g/(1 + h/R)²

This relationship can be approximated for small altitudes as:
gh = g(1 – 2h/R)

Conversely, when considering depth below Earth’s surface, gravitational acceleration decreases according to:
g’ = g × (1 – h/R)

Where h represents the depth from the surface.

These altitude and depth variations in acceleration due to gravity become crucial factors in satellite orbital mechanics and other advanced gravitation physics problems. At Earth’s center, gravitational acceleration reaches zero, representing the theoretical point where gravitational forces from all directions cancel each other completely.

Gravitational Fields, Potential, and Energy Concepts: Gravitation Class 11 Physics Problems with Solutions

A gravitational field represents the space around a massive body where its gravitational influence can be detected by other objects. This concept is fundamental to understanding gravitation physics problems and provides a framework for analyzing gravitational interactions without requiring the presence of a test mass.

Gravitational field intensity, denoted as Eg or I, quantifies the strength of this gravitational influence at any specific point. It is mathematically defined as the gravitational force experienced per unit mass at that location, expressed as Eg = F/m. This relationship allows physicists to characterize the gravitational environment independently of the object being influenced.

For a point mass or spherically symmetric body of mass M, the gravitational field intensity at distance r is given by Eg = GM/r², where G represents the universal gravitational constant. This inverse square relationship demonstrates that field intensity decreases rapidly with distance from the source mass.

Gravitational field intensity is fundamentally a vector quantity, always directed toward the center of gravity of the source mass. Its SI unit is N/m (newtons per meter), and the dimensional formula is [LT⁻²]. This vectorial nature is crucial when solving gravitational field problems involving multiple masses, as field intensities must be added vectorially.

An important application involves defining gravitational mass through the relationship Mg = Fg/g = W/g, where gravitational mass equals the weight of a body divided by the acceleration due to gravity.

Understanding Gravitational Potential and Its Properties: Gravitation Class 11 Physics Problems with Solutions

Now that we have covered gravitational field intensity, let’s examine gravitational potential, which provides another powerful approach to analyzing gravitational systems. Gravitational potential (Vg) at any point in space represents the work done per unit mass required to transport a light body from infinity to that specific location.

The mathematical expression for gravitational potential is Vg = W/m = -GM/r, where the negative sign holds significant physical meaning. This negativity arises because work is obtained when moving an object from infinity to any finite distance in a gravitational field, reflecting the attractive nature of gravitational forces.

Unlike gravitational field intensity, gravitational potential is a scalar quantity, making calculations involving multiple sources more straightforward since scalar addition applies rather than vector addition. The SI unit for gravitational potential is J/kg (joules per kilogram), with dimensional formula [L²T⁻²].

The scalar nature of gravitational potential makes it particularly valuable in complex gravitational potential energy problems involving multiple masses. When dealing with systems containing several gravitational sources, the total potential at any point equals the algebraic sum of potentials due to individual masses, significantly simplifying computational approaches.

Calculating Gravitational Potential Energy at Different Heights: Gravitation Class 11 Physics Problems with Solutions

With this understanding of gravitational potential established, we can now explore gravitational potential energy calculations. Gravitational potential energy (U) of an object represents the total work required to bring that object from infinity to its current position within a gravitational field.

The fundamental expression for gravitational potential energy is U = -GMm/r, where M represents the source mass, m is the object’s mass, and r is the separation distance. The negative sign indicates that potential energy decreases as the distance from the gravitational source increases, consistent with the attractive nature of gravitational interactions.

For objects at height h above Earth’s surface, the gravitational potential energy becomes more complex: Uh = -GMm/(R + h), where R represents Earth’s radius. This expression can be approximated as Uh = mgR/(1 + h/R) for practical calculations, particularly useful in satellite orbital mechanics and escape velocity calculations.

This height-dependent relationship proves essential when analyzing planetary motion problems and determining energy requirements for space missions. The potential energy variation with altitude directly influences spacecraft trajectories and orbital mechanics, making these calculations fundamental to aerospace applications and advanced gravitation physics problems.

Satellite Mechanics and Orbital Dynamics: Gravitation Class 11 Physics Problems with Solutions

Orbital velocity represents the minimum velocity required for a satellite to successfully enter and maintain a given orbit around Earth. This critical parameter is calculated using the formula vo = √GM/r = R√g/(R + h), where G is the gravitational constant, M is Earth’s mass, r is the orbital radius, R is Earth’s radius, and h is the height above Earth’s surface.

For satellites orbiting near Earth’s surface, the orbital velocity simplifies to vo = √gR = 7.92 km/s. This fundamental calculation forms the basis for understanding satellite orbital mechanics and is essential when solving gravitation physics problems involving artificial satellites.

The relationship between a satellite’s actual speed and its orbital velocity determines the type of trajectory it will follow:

• If v ＜ vo: The satellite follows a parabolic path and inevitably falls back to Earth

• If v = vo: The satellite maintains a stable circular orbit

• If vo ＜ v ＜ ve (escape velocity): The satellite follows an elliptical orbit

The orbital period of a satellite is determined by T = 2π√r³/GM = 2π√(R + h)³/g. For satellites near Earth’s surface, this period becomes T = 2π√R/g, which equals approximately 84 minutes—a crucial benchmark for understanding low Earth orbit dynamics.

Understanding Geostationary and Polar Satellite Systems: Class 11 Gravitation Concept Explained

Artificial satellites are primarily categorized into two distinct operational types based on their orbital characteristics and applications.

Geostationary (Parking) Satellites represent one of the most commercially valuable satellite configurations. These satellites appear stationary relative to an observer on Earth’s surface because they revolve in equatorial orbits with the same angular velocity as Earth’s rotation. Key specifications include:

These satellites serve primarily communication purposes, with notable examples including INSAT 2B and INSAT 2C, making them indispensable for modern telecommunications infrastructure.

Polar Satellites operate in polar orbits with a 90° inclination relative to the equatorial plane. Their specifications differ significantly:

Polar satellites excel in weather forecasting, atmospheric studies, and geographical mapping applications, with the PSLV series representing prominent examples of this satellite category.

Calculating Total Energy and Binding Energy of Satellites: Class 11 Gravitation Concept Explained

The total energy of a satellite in orbit represents the sum of its kinetic and potential energies, providing crucial insights into orbital stability and energy requirements. The total energy is expressed as:

E = KE + PE = GMm/2r + (-GMm/r) = -GMm/2r

This negative total energy indicates that the satellite is gravitationally bound to Earth, with the magnitude representing the energy deficit compared to a free particle at infinite distance.

Binding energy quantifies the minimum energy required to completely remove a satellite from its current orbit to infinity. This parameter is calculated as:

BE = +GMm/2r

Understanding these energy relationships is fundamental for satellite orbital mechanics calculations and provides the theoretical foundation for mission planning, orbit transfers, and satellite deployment strategies. The binding energy concept particularly helps engineers determine fuel requirements for satellite repositioning or deorbiting maneuvers.

Escape Velocity and Interplanetary Motion: Gravitation Class 11 Physics Problems with Solutions

Escape velocity represents the minimum vertical projection velocity required for a body to completely escape a celestial object’s gravitational field without ever returning. The mathematical derivation yields the formula ve = √(2GM/R), where G is the gravitational constant, M is the mass of the celestial body, and R is its radius. This formula can also be expressed as ve = √(2gR), where g represents the acceleration due to gravity at the surface.

A remarkable characteristic of escape velocity calculations is that the result remains independent of the escaping body’s mass, shape, size, or even the direction of projection. This means a feather and a spacecraft require the same escape velocity from Earth, assuming no atmospheric resistance. For our planet, this critical value equals 11.2 km/s, making it one of the most important constants in gravitation physics problems.

Relationship Between Escape Velocity and Orbital Velocity: Gravitation Class 11 Physics Problems with Solutions

The mathematical relationship connecting escape velocity and orbital velocity follows a precise formula: ve = √2 vo. This relationship proves essential when analyzing satellite orbital mechanics and determining launch requirements for space missions.

When examining different trajectory scenarios, the projection velocity determines the path a body will follow. If the initial velocity exactly equals escape velocity (v = ve), the object follows a parabolic trajectory, gradually slowing but never returning. However, when the projection velocity exceeds escape velocity (v ＞ ve), the body escapes along a hyperbolic path, maintaining excess velocity even at infinite distance from the gravitational source.

Escape Velocities for Different Celestial Bodies: JEE Main Gravitation Questions

Understanding escape velocity calculations across various celestial bodies reveals fascinating insights into planetary motion problems and gravitational field variations. The stark differences in these values reflect the diverse gravitational environments throughout our solar system and beyond.

These values demonstrate the extreme gravitational variations across different astronomical objects. The Moon’s relatively low escape velocity explains why lunar missions require significantly less energy for return trips, while Jupiter’s massive gravitational field demands substantially higher velocities. The neutron star’s extraordinary escape velocity of 2 × 10⁵ km/s illustrates the incredible gravitational intensity of these collapsed stellar remnants, approaching relativistic speeds where classical physics begins to break down.

Kepler’s Laws and Planetary Motion Analysis: JEE Main Gravitation Questions

Every planet revolves around the sun in an elliptical orbit, with the sun at one of its foci. This fundamental principle revolutionized our understanding of planetary motion and forms the cornerstone of modern celestial mechanics. Unlike the previously accepted circular orbit theory, Kepler’s first law demonstrates that planetary paths follow elliptical trajectories, explaining the varying distances between planets and the sun throughout their orbital cycles.

The elliptical nature of orbits means that planets experience perihelion (closest approach to the sun) and aphelion (farthest distance from the sun) during their revolution. This orbital geometry directly impacts gravitational forces and orbital velocities, creating the foundation for solving complex planetary motion problems in gravitation physics problems.

Law of Equal Areas and Areal Velocity Calculations: Gravitation Class 11 Physics Problems with Solutions

The radius vector drawn from the sun to a planet sweeps out equal areas in equal intervals of time, establishing that the areal velocity of the planet around the sun remains constant. This areal velocity can be mathematically expressed as dA/dt = L/2m, where L represents the angular momentum and m denotes the planet’s mass.

This law has profound implications for orbital mechanics, as it demonstrates that planets move faster when closer to the sun and slower when farther away. The constant areal velocity principle becomes essential when analyzing satellite orbital mechanics and calculating precise orbital parameters. For Kepler’s laws physics applications, this relationship allows physicists to determine instantaneous velocities at any point along an elliptical orbit, making it invaluable for mission planning and gravitational analysis.

Law of Periods and Orbital Time Relationships: Gravitation Class 11 Physics Problems with Solutions

The square of the time period (T) of a planet’s revolution around the sun is directly proportional to the cube of the semi-major axis (a) of its elliptical orbit. This relationship is expressed as T² ∝ a³ or in comparative form as (T₁/T₂)² = (a₁/a₂)³.

This law provides a powerful tool for analyzing orbital relationships throughout the solar system and beyond. By measuring either the orbital period or the semi-major axis of a celestial body, astronomers can calculate the other parameter with remarkable precision. The law applies universally to all gravitationally bound systems, making it essential for understanding both natural planetary systems and artificial satellite networks. This mathematical relationship becomes particularly valuable when solving gravitation physics problems involving multiple orbital bodies and comparative planetary analysis.

Special Gravitational Phenomena and Weightlessness: Gravitation Class 11 Notes

Weightlessness represents a fascinating phenomenon in gravitation physics problems where the effective weight of a body becomes zero. This condition occurs under specific circumstances that are crucial for understanding advanced gravitational concepts.

The primary condition creating weightlessness is free fall under gravity. When an object falls freely, it experiences no contact forces, making its effective weight zero even though gravitational force continues to act upon it. This principle extends to more complex scenarios in space technology applications.

Inside spacecraft or satellites, astronauts experience weightlessness because both they and their vehicle are in continuous free fall around Earth. The spacecraft’s orbital motion creates a perpetual falling state, eliminating the sensation of weight for all occupants. This condition is essential for understanding satellite orbital mechanics and space mission planning.

Another theoretical condition exists at the center of the Earth, where gravitational forces from all directions would cancel out, resulting in zero effective weight. Additionally, freely falling elevators demonstrate weightlessness effects, where passengers experience zero effective weight during the fall phase.

These conditions are fundamental to solving gravitation physics problems involving weightlessness scenarios and help students understand the distinction between gravitational force and effective weight in various reference frames.

Comparing Inertial Mass and Gravitational Mass: Gravitation Class 11 Physics Problems with Solutions

Understanding the relationship between inertial mass and gravitational mass is crucial for mastering advanced gravitation physics problems and represents one of the most profound principles in physics.

Inertial mass is defined as the ratio of applied force to the resulting acceleration (F/a). This mass measure relates to an object’s resistance to acceleration and remains consistent regardless of location or surrounding gravitational fields.

Gravitational mass, conversely, is defined as the weight of a body divided by the local acceleration due to gravity (W/g). This mass measure determines how strongly an object interacts with gravitational fields.

Despite their different definitions, these two masses are equal in magnitude – a principle known as the equivalence principle. This equality forms the foundation for Einstein’s general relativity theory.

The key distinction lies in their response to environmental factors. Gravitational mass is affected by the presence of other bodies nearby, while inertial mass remains unaffected by external gravitational influences. This difference becomes particularly important when solving complex gravitational field problems involving multiple massive objects.

Practical Applications in Space Technology: Gravitation Class 11 Physics Problems with Solutions

The principles of weightlessness and mass equivalence find extensive applications in modern space technology, though specific technological implementations require detailed engineering considerations beyond basic gravitational physics problems.

Space missions rely heavily on understanding weightlessness conditions for crew training, equipment design, and mission planning. The prolonged weightlessness environment in orbital spacecraft affects everything from human physiology to fluid behavior, requiring specialized solutions based on gravitational physics principles.

Satellite design incorporates these gravitational phenomena to ensure proper functionality in weightless environments. Communication satellites, weather monitoring systems, and scientific instruments must account for the absence of gravitational orientation references.

The distinction between inertial and gravitational mass becomes particularly relevant in precision spacecraft navigation and trajectory calculations, where small mass variations can significantly impact mission success over long distances and time periods.

The practical applications of these gravitational principles extend far beyond academic exercises, influencing modern space exploration, satellite communications, and our understanding of celestial mechanics. With gravitational acceleration varying from 2.3 km/s on the Moon to 618 km/s on the Sun, these concepts provide the mathematical framework necessary for missions ranging from geostationary satellites to interplanetary travel. Master these fundamental relationships between mass, distance, velocity, and energy, and you’ll possess the tools to tackle any gravitation physics problem with confidence and precision.