Gravitation Class 11 Physics: Complete Guide, All Formulas & Free PDF Download (JEE & NEET)
Gravitation — Competishun
Gravitation Class 11 Physics: Complete Guide, All Formulas & Free PDF Download (JEE & NEET)
Gravitation is one of the most fundamental and scoring chapters in Class 11 Physics. It carries significant weightage in JEE and NEET, with 2-3 questions appearing every year from this chapter. Gravitation is the force of attraction between any two masses in the universe.
This guide covers Newton's law of universal gravitation, gravitational field and potential, acceleration due to gravity, escape velocity, satellites, Kepler's laws of planetary motion, and shell theorems. Understanding these concepts is essential for solving problems in mechanics and for understanding more advanced topics like orbital mechanics.
This page gives you the complete guide to Gravitation with all concepts explained in depth. You will find clear definitions, formulas, visual diagrams, and practice questions. Download the free PDF below and keep it handy for quick revision before your JEE Main, JEE Advanced, or NEET exam.
Download the Gravitation Complete Guide PDF
Get all Gravitation concepts, formulas, Newton's law, field, potential, escape velocity, satellites, and Kepler's laws in one clean PDF, free. Perfect for JEE and NEET revision.
Download Free PDFNewton's Law of Universal Gravitation
Newton's Law
Vector Form
Gravitational Constant
Properties
Shell Theorems — Why Point Masses Work
- Theorem 1: A uniform spherical shell attracts an external particle as if its whole mass sat at the centre.
- Theorem 2: It exerts zero net force on any particle placed inside it.
- Solid Sphere: A solid sphere is a stack of such shells, so for two uniform spheres the distance is simply the centre-to-centre distance, whatever their sizes.
Gravitational Field Intensity — The Force Field
Field Intensity
Field at Earth's Surface
Between Two Masses
Solid Sphere (Inside)
Solid Sphere (Outside)
Shell (Inside)
Acceleration Due to Gravity — g and Its Variations
g at Surface
g at Height h
g at Depth d
g on Other Planets
Escape Velocity — Breaking Free from Gravity
Escape Velocity
In Terms of g
For Earth
For Moon
Kepler's Laws of Planetary Motion
- Law of Orbits: Every planet moves in an elliptical orbit with the Sun at one focus.
- Law of Areas: The radius vector drawn from the Sun to the planet sweeps out equal areas in equal times. This implies angular momentum is conserved.
- Law of Periods: The square of the orbital period (T) is proportional to the cube of the semi-major axis (a) of the orbit: T² ∝ a³.
Satellites — Orbital Motion
Orbital Velocity
Time Period
Geostationary Orbit
Energy of Satellite
Practice Questions — From JEE and NEET
| Question | Answer |
|---|---|
| Q1: Find the gravitational force between two masses of 10 kg and 20 kg separated by 1 m. (G = 6.67 × 10⁻¹¹) | F = Gm₁m₂/r² = 6.67×10⁻¹¹ × 10 × 20 / 1 = 1.33 × 10⁻⁸ N. |
| Q2: What is the gravitational field intensity at a distance of 2R from the centre of Earth? (Earth's radius = R) | E = GM/(2R)² = GM/4R² = g/4. |
| Q3: Calculate the escape velocity from Earth. (g = 9.8 m/s², R = 6.4 × 10⁶ m) | v = √(2gR) = √(2 × 9.8 × 6.4×10⁶) = 11.2 km/s. |
| Q4: What is the period of a satellite orbiting at a distance of 2R from Earth's centre? (T₀ = period of satellite at R) | T = T₀ × (2R/R)^(3/2) = 2√2 T₀. |
| Q5: A planet has mass 3M and radius 2R. What is its surface gravity? | g' = G(3M)/(2R)² = 3GM/4R² = ¾ g. |
| Q6: What is the gravitational potential energy of a mass m at height h above Earth's surface? | U = −GMm/(R+h). |
| Q7: Two masses m and 4m are separated by distance d. Where is the gravitational field zero? | x = d/3 from m (or 2d/3 from 4m). |
| Q8: What is the orbital velocity of a satellite at Earth's surface? (R = 6.4 × 10⁶ m) | v₀ = √(gR) = √(9.8 × 6.4×10⁶) = 7.9 km/s. |
| Practise these types of questions to become comfortable with applying Gravitation concepts in exam scenarios. | |
All Gravitation Formulas at a Glance
| Category | Formula |
|---|---|
| Newton's Law | F = Gm₁m₂/r² |
| Field Intensity | E = GM/r² |
| g at Surface | g = GM/R² |
| g at Height | g' = g·R²/(R+h)² |
| g at Depth | g' = g·(1 − d/R) |
| Escape Velocity | vesc = √(2GM/R) |
| Orbital Velocity | v₀ = √(GM/r) |
| Time Period | T = 2π√(r³/GM) |
| Kepler's Third Law | T² ∝ a³ |
| Energy (Satellite) | E = −GMm/(2r) |
| Potential Energy | U = −GMm/r |
| Gravitational Constant | G = 6.67 × 10⁻¹¹ N·m²/kg² |
| Memorise these formulas for Gravitation. They are the key to scoring full marks in this chapter. | |
Common Mistakes in Gravitation
- Confusing G and g: G is the universal gravitational constant (6.67 × 10⁻¹¹), while g is the acceleration due to gravity (9.8 m/s² on Earth).
- Using centre of mass for distance: For uniform spheres, use centre-to-centre distance. For irregular bodies, you must integrate.
- Forgetting the negative sign in potential energy: Gravitational potential energy is always negative: U = −GMm/r.
- Confusing escape velocity with orbital velocity: Escape velocity is √2 times the orbital velocity. v_esc = √2 · v₀.
- Misapplying Kepler's laws: Kepler's laws apply to orbits under gravity. T² ∝ a³ only for orbits around the same central mass.
- Forgetting field superposition: Gravitational fields add as vectors. The net field at a point is the vector sum of all individual fields.
Why Gravitation Matters for JEE and NEET
- High weightage: This chapter appears in 2-3 questions in every JEE Main, JEE Advanced, and NEET physics paper.
- Foundation for mechanics: Understanding gravitation is essential for understanding orbital mechanics, satellite motion, and celestial mechanics.
- Conceptual clarity: This chapter rewards students who understand the concepts rather than just memorizing formulas.
- Practical relevance: Gravitation explains everything from the motion of planets and satellites to tides and the structure of the universe.
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