Class 9 Physics Chapter 9 Gravitation — Formulas & Key Points
Chapter 9 Gravitation in CBSE Class 9 Physics introduces the universal force that governs motion from falling apples in Patna to orbiting satellites. This formula sheet consolidates every equation, definition, constant, and application you need for exams, homework, and conceptual clarity. Whether you are revising Newton's law of universal gravitation, calculating weight on different planets, or understanding why astronauts float, this page serves as your single-stop reference anchored in NCERT terminology and the 2025 CBSE syllabus.
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Key takeaways
- ✓Newton's law of universal gravitation states that F = G(m₁m₂)/r², where G = 6.67 × 10⁻¹¹ N·m²/kg² is a universal constant applicable everywhere in the universe.
- ✓Weight (W = mg) is the gravitational force on an object and varies by location; mass remains constant everywhere and is measured in kilograms.
- ✓Acceleration due to gravity g ≈ 9.8 m/s² on Earth's surface; it decreases with height and varies slightly with latitude due to Earth's shape and rotation.
- ✓In free fall, all objects accelerate at the same rate (g) regardless of mass, because gravitational force and inertia exactly cancel out.
- ✓Gravitational force acts between any two masses in the universe; the force is attractive, acts along the line joining the centers, and obeys an inverse-square law.
- ✓Common mistakes include confusing mass (kg) with weight (N), using wrong units for G, and forgetting to square the distance in the denominator.
- ✓For quick problem-solving, remember: double the distance → force becomes one-fourth; double both masses → force becomes four times stronger.
Core Formulas and Laws — Master Table
Every formula in NCERT Class 9 Physics Chapter 9 Gravitation is listed below with its statement, variables, SI units, and when to apply it. This table is your go-to reference during problem-solving. Remember that gravitational force applies universally to any two masses, weight depends on local gravity, and free-fall acceleration g is approximately 10 m/s² on Earth for ease of calculation (use 9.8 m/s² when specified). Each formula connects to real-world phenomena—satellite orbits, tides, planetary motion, and everyday weight measurement. Master these, and you have mastered the chapter.
- Newton's Law of Universal Gravitation: F = G(m₁m₂)/r² — calculates attractive force between any two masses separated by distance r.
- Weight formula: W = mg — relates gravitational force (weight in Newtons) to mass (kg) and local acceleration due to gravity.
- Acceleration due to gravity on Earth's surface: g = GM/R² — derived by equating gravitational force to weight; M is Earth's mass, R is Earth's radius.
- Value of g decreases with height: gₕ ≈ g(1 − 2h/R) for small h — used when calculating gravity at altitude (mountains, aircraft).
- Free-fall condition: net force = mg, acceleration = g — applies when only gravity acts; all objects fall at same rate in vacuum.
- Universal gravitational constant: G = 6.67 × 10⁻¹¹ N·m²/kg² — a fundamental constant of nature, same everywhere in the universe.
Key Terms and Definitions
Understanding precise definitions is critical for CBSE exams and NCERT-based assessments. Gravitation refers to the universal attractive force between masses; it is not limited to Earth. Gravitational force is the actual measurable pull calculated using Newton's law. Weight is often confused with mass—weight is a force (measured in Newtons) that changes with location, while mass is invariant (measured in kilograms). Acceleration due to gravity g quantifies how fast objects accelerate under gravity alone. Free fall describes motion where gravity is the only force acting; in this state, all objects accelerate equally regardless of mass. The universal gravitational constant G is one of nature's fundamental constants, linking force, mass, and distance in gravitational interactions across the cosmos.
- Gravitation: The force of attraction acting between any two objects in the universe solely due to their masses.
- Gravitational Force: The actual force calculated by F = G(m₁m₂)/r²; always attractive, acts along the line joining centers of the two masses.
- Weight (W): The gravitational force exerted by a planet (usually Earth) on an object; W = mg; measured in Newtons.
- Mass (m): Amount of matter in an object; intrinsic property; remains constant on Earth, Moon, or anywhere; measured in kilograms.
- Acceleration Due to Gravity (g): Rate of acceleration of a freely falling object near a planet's surface; approximately 9.8 m/s² on Earth.
- Free Fall: Motion under gravity alone with no air resistance or other forces; all objects in free fall accelerate at g.
- Universal Gravitational Constant (G): 6.67 × 10⁻¹¹ N·m²/kg²; a fundamental constant appearing in Newton's law of universal gravitation.
- Normal Force: The contact force perpendicular to a surface; when you stand on a scale, it measures normal force, which equals your weight if stationary.
Important Constants and Values
Certain numerical values appear repeatedly in Class 9 Physics Chapter 9 Gravitation problems. Memorise these constants and Earth-specific values to speed up calculations. The universal gravitational constant G is tiny, which explains why gravitational attraction between everyday objects (books, people) is negligible. Earth's mass and radius are used to derive g at the surface. The standard value g = 9.8 m/s² is often approximated to 10 m/s² in CBSE exams for simpler arithmetic—always check the question to see which value to use. Knowing the Moon's surface gravity (about one-sixth of Earth's) helps solve comparative weight problems. These constants are drawn directly from NCERT Class 9 Physics and are valid for 2025 CBSE exams.
- Universal Gravitational Constant: G = 6.67 × 10⁻¹¹ N·m²/kg² (memorise this; it appears in almost every numerical problem).
- Acceleration due to gravity on Earth's surface: g ≈ 9.8 m/s² (exact) or g ≈ 10 m/s² (approximation for easier calculation).
- Mass of Earth: M ≈ 6 × 10²⁴ kg (used to calculate gravitational force or derive g).
- Radius of Earth: R ≈ 6.4 × 10⁶ m or 6400 km (used in g = GM/R² and height variation problems).
- Acceleration due to gravity on Moon's surface: g(Moon) ≈ 1.6 m/s² or approximately g(Earth)/6.
- Standard units: Force in Newtons (N), mass in kilograms (kg), distance in meters (m), acceleration in m/s².
Memory Tricks and Mnemonics
Remembering formulas and concepts becomes easier with smart mnemonics. For Newton's law F = G(m₁m₂)/r², think 'Force Grows with Mass, but Dies with Distance squared'—bigger masses increase F, but doubling distance cuts F to one-fourth. To recall that weight W = mg, remember 'Weight is Mass times Gravity'. For the universal constant G, the digits 667 appear (6.67 × 10⁻¹¹); link it to 'Six-Six-Seven in the tiny negative eleven'. To distinguish mass from weight, use 'Mass is Me (intrinsic), Weight is Where I am (depends on location)'. These tricks are popular among Patna and Delhi coaching centres and help during last-minute revision before CBSE board or school exams.
- F = G(m₁m₂)/r²: 'Big Masses pull More, but Distance Dilutes it Down' (inverse-square law).
- W = mg: 'Weight is What the Ground feels when you stand' (the force you push down with).
- G = 6.67 × 10⁻¹¹: Remember '667 negative eleven' or 'Six-Six-Seven very very small'.
- Mass vs Weight: 'Mass is Matter, Weight is Where' — mass stays same, weight changes with planet.
- Free fall: 'Feather and Hammer Fall the same in a vacuum' — no mass dependence.
- g decreases with height: 'Higher you go, Lighter you get' (slightly smaller g at altitude).
- Inverse-square: 'Double Distance, Quarter Force' — a powerful shortcut for quick checks.
Common Mistakes: Signs, Units, and Notation
Students lose marks in CBSE Class 9 Physics exams by mixing units, dropping the square on r, or confusing mass with weight. Always write units alongside numerical answers: force in Newtons (N), mass in kilograms (kg), distance in meters (m). A frequent error is using centimeters or kilometers without converting to meters first. Another pitfall: forgetting to square the distance r in F = G(m₁m₂)/r²—students often divide by r instead of r². When substituting G, include the full exponent 10⁻¹¹; leaving it out turns your answer wrong by 11 orders of magnitude. In problems involving height, ensure you use the distance from Earth's center (R + h), not just height h, unless the formula already accounts for it. Finally, weight must always be in Newtons; writing 'my weight is 60 kg' is technically incorrect—60 kg is mass, weight is 600 N.
- Unit mismatch: Convert all distances to meters (m) before substituting into formulas; 1 km = 1000 m, 1 cm = 0.01 m.
- Forgetting to square r: In F = G(m₁m₂)/r², the denominator is r squared, not just r; double-check your calculation.
- Confusing mass and weight: Mass is in kg (scalar), weight is in N (force); never write 'weight = 50 kg'.
- Omitting exponent in G: G = 6.67 × 10⁻¹¹; if you write 6.67 without the exponent, your answer will be astronomically wrong.
- Using wrong g value: Check if the problem specifies g = 9.8 m/s² or g = 10 m/s²; stick to what is given.
- Distance from center vs height: When calculating gravitational force, use r = distance between centers, not just altitude above surface.
- Sign convention: Gravitational force is always attractive (no negative sign needed in magnitude calculations).
Solved Mini-Example 1: Gravitational Force Between Two Masses
Problem: Two iron spheres of mass 40 kg and 60 kg are placed 0.5 m apart. Calculate the gravitational force between them. Use G = 6.67 × 10⁻¹¹ N·m²/kg². This is a direct application of Newton's law of universal gravitation and tests your ability to substitute values correctly and handle scientific notation. Always write every step, especially in CBSE board exams, to claim partial marks even if the final answer has a small arithmetic error. This type of numerical appears frequently in NCERT exercises and CBSE sample papers.
- Step 1: Write down given values: m₁ = 40 kg, m₂ = 60 kg, r = 0.5 m, G = 6.67 × 10⁻¹¹ N·m²/kg².
- Step 2: Apply formula F = G(m₁m₂)/r².
- Step 3: Calculate numerator: m₁m₂ = 40 × 60 = 2400 kg².
- Step 4: Calculate denominator: r² = (0.5)² = 0.25 m².
- Step 5: Substitute: F = 6.67 × 10⁻¹¹ × (2400 / 0.25) = 6.67 × 10⁻¹¹ × 9600.
- Step 6: Multiply: F = 6.4032 × 10⁻⁷ N ≈ 6.4 × 10⁻⁷ N.
- Answer: The gravitational force is approximately 6.4 × 10⁻⁷ N, an extremely small force imperceptible in daily life.
Solved Mini-Example 2: Calculating Weight on Earth and Moon
Problem: A student has a mass of 50 kg. Calculate the student's weight on Earth (g = 10 m/s²) and on the Moon (g = 1.6 m/s²). This problem reinforces the distinction between mass (constant) and weight (variable). Weight is the gravitational force acting on an object, calculated by W = mg. On Earth, the student's weight is 500 N; on the Moon, it drops to 80 N because lunar gravity is weaker. Many CBSE questions ask students to compare weights on different celestial bodies to test conceptual understanding. Always specify units (Newtons for weight, kilograms for mass) to avoid losing marks.
- Given: mass m = 50 kg, g(Earth) = 10 m/s², g(Moon) = 1.6 m/s².
- Formula: W = mg.
- Weight on Earth: W(Earth) = 50 × 10 = 500 N.
- Weight on Moon: W(Moon) = 50 × 1.6 = 80 N.
- Conclusion: The student's mass remains 50 kg everywhere, but weight changes with the local value of g.
- Exam tip: If a question asks for weight, always give answer in Newtons; if it asks for mass, give kilograms.
Solved Mini-Example 3: Finding Acceleration Due to Gravity on a Planet
Problem: A planet has mass 8 × 10²³ kg and radius 4 × 10⁶ m. Calculate the acceleration due to gravity on its surface. Use G = 6.67 × 10⁻¹¹ N·m²/kg². This problem uses the derived formula g = GM/R², which comes from equating F = G(Mm)/R² and F = mg for an object of mass m on the planet's surface. Solving it tests your ability to handle large powers of ten and perform division carefully. Make sure to square the radius R correctly. Such problems appear in NCERT exercises and are common in CBSE school exams and term tests.
- Given: Mass of planet M = 8 × 10²³ kg, Radius R = 4 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg².
- Formula: g = GM/R².
- Step 1: Calculate R² = (4 × 10⁶)² = 16 × 10¹² m².
- Step 2: Substitute into formula: g = (6.67 × 10⁻¹¹ × 8 × 10²³) / (16 × 10¹²).
- Step 3: Multiply numerator: 6.67 × 8 = 53.36; exponents: 10⁻¹¹ × 10²³ = 10¹².
- Step 4: Divide: g = (53.36 × 10¹²) / (16 × 10¹²) = 53.36 / 16 = 3.335 m/s².
- Answer: The surface gravity of this planet is approximately 3.34 m/s², roughly one-third of Earth's gravity.
One-Glance Last-Minute Revision Box
This compact summary is designed for quick revision 30 minutes before your CBSE exam or school test. Read through it once, then attempt a few NCERT back-exercise problems to reinforce. The box captures every critical formula, constant, definition, and common pitfall in Chapter 9 Gravitation. Pin it above your study desk or photograph it on your phone for on-the-go revision during the metro commute or bus ride to school. It is written in plain language that a Class 9 student can understand without flipping back to heavy theory pages.
- Newton's Law: F = G(m₁m₂)/r². Force is attractive, inversely proportional to r², directly proportional to masses.
- G = 6.67 × 10⁻¹¹ N·m²/kg² — universal constant, same everywhere in the cosmos.
- Weight: W = mg. Weight is a force (Newtons), mass is constant (kilograms). W changes with planet, m does not.
- g on Earth ≈ 9.8 or 10 m/s²; on Moon ≈ 1.6 m/s². g decreases with altitude and varies slightly with latitude.
- Free fall: All objects fall at same rate g when only gravity acts; no dependence on mass. Feather = Hammer in vacuum.
- Common mistakes: forgetting to square r; mixing kg and N; omitting 10⁻¹¹ in G; using cm or km instead of m.
- Quick checks: Double distance → force becomes 1/4. Double both masses → force becomes 4×. These shortcuts save time.
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Frequently asked questions
What is the formula for Newton's law of universal gravitation?+
F = G(m₁m₂)/r², where F is the gravitational force, G = 6.67 × 10⁻¹¹ N·m²/kg² is the universal gravitational constant, m₁ and m₂ are the masses of the two objects, and r is the distance between their centers. This law applies to any two masses in the universe.
How do I calculate weight using the formula W = mg?+
Multiply the object's mass (in kilograms) by the local acceleration due to gravity g (in m/s²). For example, a 50 kg student on Earth (g = 10 m/s²) has weight W = 50 × 10 = 500 N. On the Moon (g = 1.6 m/s²), the same student weighs 50 × 1.6 = 80 N.
What is the value of the universal gravitational constant G?+
G = 6.67 × 10⁻¹¹ N·m²/kg². This constant is the same everywhere in the universe and appears in Newton's law of universal gravitation. Memorise the digits 667 and the exponent −11 for quick recall during exams.
Why do all objects fall at the same rate in free fall?+
In free fall, gravitational force F = mg produces acceleration a = F/m = g, which is independent of mass m. A feather and a hammer fall at the same rate in a vacuum because the larger force on the heavier object is exactly offset by its greater inertia. This was famously demonstrated on the Moon by astronaut David Scott.
How does g vary with height above Earth's surface?+
Acceleration due to gravity decreases with altitude. For small heights h, the approximate formula is gₕ = g(1 − 2h/R), where R is Earth's radius. For example, at the top of Mount Everest (h ≈ 9 km), g is slightly less than 9.8 m/s².
What is the difference between mass and weight?+
Mass is the amount of matter in an object, measured in kilograms, and remains constant everywhere. Weight is the gravitational force acting on that mass, calculated by W = mg, measured in Newtons, and changes with the local value of g. For instance, your mass is the same on Earth and Moon, but your weight on the Moon is about one-sixth of your Earth weight.
Can I use g = 10 m/s² instead of 9.8 m/s² in exams?+
Yes, if the problem does not specify otherwise or if it explicitly says 'take g = 10 m/s²'. Using 10 m/s² simplifies arithmetic and is acceptable in most CBSE school exams. However, if the question states 'use g = 9.8 m/s²', you must use that value for accurate marks.
What are common mistakes students make in gravitation numericals?+
Frequent errors include forgetting to square the distance r in F = G(m₁m₂)/r², confusing mass (kg) with weight (N), not converting distances to meters, omitting the 10⁻¹¹ exponent in G, and using the wrong value of g. Always write units, double-check denominators, and convert all measurements to SI units before substituting.
How is the formula g = GM/R² derived?+
Equate the gravitational force F = GMm/R² (from Newton's law) with the weight F = mg of an object of mass m on a planet's surface. Cancel m from both sides to get g = GM/R², where M is the planet's mass and R its radius. This shows that g depends only on the planet's mass and radius, not on the object's mass.
How does CBSETUTOR.ai help with Class 9 Physics Chapter 9 Gravitation?+
CBSETUTOR.ai provides instant step-by-step solutions when you upload a photo of any Gravitation problem. The AI tutor explains every formula application, unit conversion, and arithmetic step in NCERT language. It is available 24×7, covers unlimited questions, and costs just ₹999/month for all subjects across Classes 6–12. Start with a 3-day free trial to see how it works.
Related resources
Important Questions: CBSE Class 9 Physics Chapter 9 GravitationCBSE Class 9 Physics Chapter 9 Gravitation Worksheet with AnswersCBSE Class 9 Physics Chapter 9 Gravitation — 20 MCQs with Answersमहत्वपूर्ण प्रश्न: CBSE कक्षा 9 भौतिकी अध्याय 9 गुरुत्वाकर्षणCBSE Class 9 Mathematics Chapter 1 Number Systems — NotesCBSE Class 9 Mathematics — Number Systems: complete chapter guideClass 9 Physics Chapter 7: Motion – Complete Notes, Definitions & ExamplesClass 9 Mathematics Chapter 2 Polynomials — Formulas & Key Points
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