NCERT Solutions for Class 11 Physics Chapter 8 – Gravitation
Chapter 8 of Class 11 Physics, Gravitation, is a foundational chapter that explains one of the four fundamental forces of nature — gravity. Students explore how every object in the universe attracts every other object with a force that depends on their masses and the distance between them, as described by Newton's Law of Universal Gravitation. The chapter begins with a historical account of Kepler's three laws of planetary motion, which laid the groundwork for Newton's gravitational theory. Students learn to calculate gravitational force, gravitational potential energy, and the conditions under which objects achieve orbital or escape velocity. The variation of gravitational acceleration with altitude and depth is a commonly tested concept in board exams and entrance tests like JEE and NEET. Topics such as geo-stationary satellites, energy of a satellite in orbit, and weightlessness are explained with clear derivations. Mastery of this chapter helps students understand not just terrestrial mechanics but also celestial phenomena like tides, planetary motion, and satellite communication. The NCERT solutions provided here follow the CBSE curriculum and offer step-by-step answers to all textbook exercises, making revision efficient and conceptually sound.
NCERT Solutions PDF – Class 11 Physics Chapter 8 (All Exercises)
The PDF covers solutions to all exercises from the NCERT textbook including Exercise 8.1 to 8.33 (numericals and theory questions). Prepared by expert physics teachers as per the latest CBSE syllabus.
| Resource Name | Description | Best For |
|---|---|---|
| NCERT Solutions | Detailed answers and explanations for NCERT textbook questions across all classes and subjects. | Homework, assignments, and exam preparation |
| NCERT Solutions for Class 11 | Chapter-wise solutions for all Class 11 subjects including Physics, Chemistry, Mathematics, Biology, and English. | Class 11 board exam preparation |
| NCERT Solutions for Class 11 Physics | Step-by-step solutions covering all chapters such as Motion, Laws of Motion, Work Energy and Power, Thermodynamics, and Waves. | Concept building and numerical problem-solving |
| NCERT Exemplar Class 11 Physics | Advanced and application-based questions designed to strengthen conceptual understanding and analytical skills. | JEE, NEET, Olympiads, and higher-order practice |
| Physics Formula | Chapter-wise collection of important formulas, equations, and derivations for quick revision. | Last-minute revision and numerical practice |
Important Formulas – Chapter 8: Gravitation
| Formula | Expression | Description |
|---|---|---|
| Newton's Law of Gravitation | F = G·M·m / r² | Force between two masses M and m separated by distance r; G = 6.674 × 10⁻¹¹ N m² kg⁻² |
| Acceleration due to gravity | g = GM / R² | g on Earth's surface; R = radius of Earth |
| g at height h | g_h = g(1 − 2h/R) for h ≪ R | Approximate formula; decreases with altitude |
| g at depth d | g_d = g(1 − d/R) | Decreases linearly with depth; zero at center |
| Gravitational Potential Energy | U = −GMm / r | Negative sign indicates bound system |
| Orbital Velocity | v_o = √(GM/r) = √(gR²/r) | Speed needed for circular orbit at distance r from center |
| Escape Velocity | v_e = √(2GM/R) = √(2gR) | Minimum speed to escape Earth's gravity (≈11.2 km/s) |
| Time Period of Satellite | T = 2π√(r³/GM) | Kepler's Third Law applied to satellites |
| Energy of Satellite | E = −GMm / 2r | Total mechanical energy (KE + PE) in orbit |
| Kepler's Third Law | T² ∝ a³ | Square of period proportional to cube of semi-major axis |
| Gravitational Potential | V = −GM / r | Potential energy per unit mass |
Subtopics Explained – Chapter 8: Gravitation
Kepler's Laws of Planetary Motion
Kepler formulated three empirical laws based on Tycho Brahe's astronomical data. The Law of Orbits states all planets move in elliptical orbits with the Sun at one focus. The Law of Areas states the line joining a planet to the Sun sweeps equal areas in equal time intervals (conservation of angular momentum). The Law of Periods states T² ∝ a³, where a is the semi-major axis — a key formula in numerical problems.
Newton's Law of Gravitation & The Gravitational Constant
Newton generalised Kepler's findings into a universal law: every particle attracts every other with force F = GMm/r². The constant G was first measured by Cavendish using the torsion balance experiment. This law is universal — it applies from apples falling to galaxies colliding.
Acceleration Due to Gravity and Its Variation
The value of g (≈9.8 m/s²) is not constant — it varies with altitude, depth, latitude (due to Earth's rotation and shape), and even the density of local terrain. These variations are crucial for exam-oriented numerical problems.
Gravitational Potential Energy and Potential
Gravitational PE (U = −GMm/r) is always negative, signifying a bound state. Work must be done against gravity to move a mass from r to infinity. Gravitational potential V = U/m = −GM/r is the PE per unit mass.
Escape Speed and Orbital Velocity
Escape velocity is the minimum speed for an object to permanently leave a gravitational field — approximately 11.2 km/s for Earth. Orbital velocity (~7.9 km/s for near-Earth orbit) is the speed for a circular orbit; v_e = √2 × v_o.
Satellites – Geostationary and Polar
A geostationary satellite has T = 24 hours and orbits at ~36,000 km above equator, appearing stationary. Polar satellites orbit at lower altitudes (~500–800 km) and cover the entire Earth surface for remote sensing and weather monitoring.
Quick Reference Table – Key Values in Gravitation
| Quantity | Value / Formula | Remark |
|---|---|---|
| G (Gravitational Constant) | 6.674 × 10⁻¹¹ N m² kg⁻² | Universal constant (Cavendish experiment) |
| Mass of Earth (M) | 5.97 × 10²⁴ kg | Standard value |
| Radius of Earth (R) | 6.4 × 10⁶ m | Mean radius |
| g (surface) | 9.8 m/s² | Standard value at sea level |
| Escape velocity (Earth) | 11.2 km/s | Minimum to escape Earth |
| Orbital velocity (near Earth) | ~7.9 km/s | For orbit at R |
| Geostationary orbit altitude | ~35,786 km | Above equator; T = 24 h |
| Relationship | v_e = √2 · v_o | Always true at same r |
| Energy in orbit | KE = |Total Energy| | KE = GMm/2r, PE = −GMm/r |
| Weightlessness | Apparent weight = 0 | In free fall or orbital motion |
NCERT Solutions for Class 11 Physics Chapter 8: Gravitation
The universal law of gravitation states that every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. This law explains planetary motion, satellite movement, and many natural phenomena. Students learn how gravitational force acts between celestial bodies and objects on Earth. Understanding this law is essential because it forms the basis for several concepts discussed later in physics. Numerical problems based on gravitational force are among the most commonly asked examination questions.
Acceleration due to gravity is the acceleration experienced by an object when it falls freely under Earth's gravitational pull. Its standard value near Earth's surface is approximately 9.8 m/s². However, this value changes with altitude, depth, and geographical location. The chapter explains how Earth's shape and rotation influence gravitational acceleration. Understanding these variations helps students solve conceptual and numerical questions accurately. This topic is frequently included in board examinations because it combines theoretical understanding with practical applications related to motion under gravity.
Mass is the amount of matter contained in an object, while weight is the gravitational force acting on that mass. Mass remains constant regardless of location, whereas weight changes depending on the gravitational field strength. This distinction is important when studying planets, satellites, and space missions. Students often encounter numerical questions requiring conversion between mass and weight. The chapter emphasizes understanding the physical meaning of both quantities rather than simply memorizing formulas. A clear grasp of this concept helps avoid common mistakes in examination problems.
Satellites remain in orbit because the gravitational force provided by Earth acts as the necessary centripetal force required for circular motion. Instead of falling directly to Earth, satellites continuously move forward while being pulled inward by gravity. This balance creates stable orbital motion. The chapter discusses orbital velocity, geostationary satellites, and practical applications of satellite technology. Understanding orbital mechanics is important for solving numerical problems and appreciating how communication, weather forecasting, and navigation systems function effectively in modern society.
Escape velocity is the minimum speed required for an object to completely overcome a planet's gravitational pull without additional propulsion. For Earth, this value is approximately 11.2 km/s. The concept is important in understanding space exploration and rocket launches. Students learn how escape velocity depends on the mass and radius of a celestial body. Examination questions often test derivations, formulas, and applications related to escape velocity. A thorough understanding helps students connect gravitational theory with real-world scientific achievements and technological advancements.