Instructions
Total Questions: 20 | Marks: 4 each | No Negative Marking
Gravitation – IIT JEE Notes (Set 25)
Introduction to Gravitation
Definition
Gravitation is the universal force of attraction between any two masses in the universe.
Importance
It explains planetary motion, satellite motion, tides, and falling of bodies toward Earth.
Newton’s Law of Gravitation
Statement
Every particle attracts every other particle with a force directly proportional to product of their masses and inversely proportional to square of distance between them.
Formula
F = Gm₁m₂/r²
Variables
F = gravitational force
G = universal gravitational constant
m₁, m₂ = masses
r = separation between centers
Universal Gravitational Constant
Symbol
G
Value
G = 6.67 × 10⁻¹¹ Nm²/kg²
Importance
Its value remains same everywhere in the universe.
Characteristics of Gravitational Force
Main Features
Always attractive, central in nature, long range force, and obeys inverse square law.
Weak Force
Gravitational force is weakest among fundamental forces.
Acceleration Due to Gravity
Definition
Acceleration produced in a body due to Earth’s gravitational pull.
Formula
g = GM/R²
Standard Value
g ≈ 9.8 m/s²
Variation of g with Height
Relation
Acceleration due to gravity decreases with increase in height above Earth surface.
Approximate Formula
gh = g(1 – 2h/R)
Variation of g with Depth
Relation
Acceleration due to gravity decreases with depth below Earth surface.
Formula
gd = g(1 – d/R)
Important Point
g becomes zero at center of Earth.
Variation of g Due to Earth Rotation
Effect
g is maximum at poles and minimum at equator.
Reason
Centrifugal force due to Earth rotation reduces effective gravity at equator.
Mass and Weight
Mass
Amount of matter in a body and remains constant everywhere.
Weight
Force with which Earth attracts a body.
Formula
W = mg
Key Insight
Weight changes from place to place while mass remains constant.
Gravitational Potential
Definition
Work done per unit mass in bringing a body from infinity to a point.
Formula
V = -GM/r
Unit
J/kg
Gravitational Potential Energy
Definition
Energy possessed by a body due to gravitational interaction.
Formula
U = -GMm/r
Important Point
Potential energy is negative because gravitational force is attractive.
Escape Velocity
Definition
Minimum velocity required for a body to escape Earth’s gravitational field permanently.
Formula
ve = √(2GM/R)
Value for Earth
Approximately 11.2 km/s.
Important Point
Escape velocity is independent of mass of body.
Orbital Velocity
Definition
Velocity required for satellite to remain in stable orbit around Earth.
Formula
v = √(GM/R)
Value Near Earth
Approximately 7.9 km/s.
Satellites
Definition
Objects revolving around planets under gravitational attraction.
Natural Satellites
Moon is natural satellite of Earth.
Artificial Satellites
Man-made satellites used for communication, weather, and navigation.
Geostationary Satellite
Definition
Satellite appearing stationary relative to Earth.
Conditions
Orbital period must be 24 hours and orbit must lie in equatorial plane.
Applications
Communication and weather forecasting.
Kepler’s Laws of Planetary Motion
First Law
Planets move in elliptical orbits with Sun at one focus.
Second Law
Line joining Sun and planet sweeps equal areas in equal intervals of time.
Third Law
Square of orbital period is proportional to cube of semi-major axis.
T² ∝ R³
Weightlessness
Definition
Condition when apparent weight becomes zero.
Cause in Satellites
Satellites and astronauts remain in continuous free fall.
Energy of Satellite
Kinetic Energy
K = GMm/2R
Potential Energy
U = -GMm/R
Total Energy
E = -GMm/2R
Gravitational Field Intensity
Definition
Force experienced by unit mass placed at a point.
Formula
E = GM/r²
Unit
N/kg
Tides
Cause
Tides are caused mainly due to gravitational pull of Moon and Sun.
Types
High tide and low tide.
Conceptual Insights
Key Understanding
Gravitational force governs motion of celestial bodies and keeps planets and satellites in orbit.
Common Mistakes
Students often confuse orbital velocity with escape velocity and misuse signs in gravitational potential energy.
Important Exam Concepts
Conceptual Traps
Escape velocity is √2 times orbital velocity near Earth surface.
JEE Strategy
Practice derivations, satellite motion numericals, Kepler’s laws, and variation of g thoroughly for IIT JEE preparation.