Gravitation is one of the most fundamental chapters in Class 11 Physics. It explains the force of attraction between masses, which governs the motion of planets, satellites, and objects on Earth.
This chapter is very important for:
- CBSE Board Exams
- JEE (Main + Advanced)
- NEET
👉 Core Idea: Every object in the universe attracts every other object with a force called gravitational force.
1. Universal Law of Gravitation
Definition
Every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Formula
F = G (m₁m₂ / r²)
Where:
- G = universal gravitational constant
- m₁, m₂ = masses
- r = distance
Value of G
G = 6.67 × 10⁻¹¹ N·m²/kg²
Concept Clarity
👉 WHY inverse square law?
Because gravitational force spreads in space → decreases with square of distance.
2. Gravitational Force Characteristics
- Always attractive
- Long-range force
- Conservative force
- Central force
3. Acceleration Due to Gravity (g)
Definition
Acceleration experienced by a body due to Earth’s gravitational force.
Formula
g = GM/R²
Value
g ≈ 9.8 m/s²
Variation of g
With Height
g decreases as height increases
With Depth
g decreases as depth increases
With Latitude
g varies due to Earth’s rotation
4. Free Fall
Definition
Motion of a body under gravity alone.
Equations
v = u + gt
s = ut + (1/2)gt²
v² = u² + 2gs
5. Gravitational Potential Energy
Definition
Energy possessed by a body due to gravitational position.
Formula
PE = -GMm/r
Concept Clarity
Negative sign indicates energy is required to separate objects.
6. Escape Velocity (Very Important)
Definition
Minimum velocity required to escape Earth’s gravitational field.
Formula
vₑ = √(2GM/R)
Value
≈ 11.2 km/s
Concept Clarity
👉 WHY independent of mass?
Because mass cancels in derivation.
7. Orbital Velocity
Definition
Velocity required for satellite to stay in orbit.
Formula
v = √(GM/R)
Relation
vₑ = √2 × v
8. Satellites
Types
Geostationary Satellite
- Period = 24 hours
- Fixed over one point
Polar Satellite
- Moves around poles
Applications
- Communication
- Weather forecasting
- GPS
9. Kepler’s Laws of Planetary Motion
First Law
Planets move in elliptical orbits
Second Law
Equal areas in equal time
Third Law
T² ∝ R³
10. Weightlessness
Definition
Condition when apparent weight becomes zero.
👉 Occurs in orbit due to free fall.
Important Numericals (CBSE + JEE Level)
Numerical 1
Find gravitational force between two 1 kg masses separated by 1 m
F = G(1×1)/1² = 6.67×10⁻¹¹ N
Numerical 2
Find g if Earth mass and radius are given
g = GM/R²
Numerical 3
Find escape velocity if g = 10 m/s² and R = 6400 km
vₑ = √(2gR)
Numerical 4
Find orbital velocity at Earth surface
v = √(gR)
Important Formula Sheet
- F = Gm₁m₂/r²
- g = GM/R²
- vₑ = √(2GM/R)
- v = √(GM/R)
- PE = -GMm/r
JEE / NEET Focus
- Escape velocity
- Variation of g
- Satellite motion
CBSE Board Strategy
- Write laws clearly
- Practice numericals
- Learn derivations
Common Mistakes
- Ignoring negative sign in PE
- Confusing orbital and escape velocity
- Unit errors