Gravitation — NEET/JEE Complete Master Guide

🌍

⚛ NEET / JEE Physics · Chapter 8

Gravitation Complete Master Guide

From daily-life intuition to satellite orbits — with visual diagrams, all formulas, and 30 practice MCQs

Sections

Formulas

MCQs

3–5

NEET Qs/yr

▼ scroll to begin

G = 6.67×10⁻¹¹

Zero Level · Foundation

WHY DO THINGS FALL?

Build solid intuition before touching equations. Real understanding starts here.

🍎 The Apple Story (Real Meaning): Newton saw an apple fall and asked — "If Earth pulls the apple, does it also pull the Moon? And if yes, why doesn't the Moon crash into us?" That single question changed physics forever and gave us the Universal Law of Gravitation.

🌙 Moon constantly falls but misses Earth?
The Moon moves sideways (tangential velocity) AND falls toward Earth simultaneously. These two motions combine into a perfect orbit. Imagine throwing a ball so fast that as it falls, Earth curves away beneath it — that's exactly what the Moon does, every second.

Mass vs Weight — The #1 Confusion

❌ Wrong Thinking

"Mass and weight are the same thing. 60 kg on Earth = 60 kg on the Moon."

✅ Correct

Mass = amount of matter (kg) — never changes anywhere.
Weight = mg (N) — changes with location. On Moon = 1/6th of Earth weight!

Mass (m)

Unit: kg · Same on Earth, Moon, deep space · Scalar · Can never be zero

Weight (W)

Unit: Newton · W = mg · Becomes 0 in zero-gravity · Vector quantity

Gravitation

Universal force between ANY two masses — Sun-Earth, Earth-Moon, you-your phone

Gravity

Earth's specific pull on nearby objects. A special case of gravitation, not a different force

Core Law

NEWTON'S LAW

Every mass in the universe attracts every other mass.

F = G · m₁ · m₂ / r²

Force of attraction between two point masses separated by distance r

G — Universal Constant

G = 6.67 × 10⁻¹¹ N m² kg⁻²

Tiny value! That's why you don't feel pulled toward your friend. Only planetary-scale masses create noticeable gravity.

r² — Inverse Square Law

Double distance → Force = F/4
Triple distance → Force = F/9
10× distance → Force = F/100

Force spreads over sphere surface (4πr²). Larger sphere = weaker force.

Why Inverse Square? — Visual Proof

[G] = M⁻¹ L³ T⁻²

From G = Fr²/(m₁m₂) → [MLT⁻²·L²] / [M²] = M⁻¹L³T⁻²

💡 Never confuse G and g:
G = 6.67×10⁻¹¹ — universal constant, NEVER changes anywhere in the universe.
g = 9.8 m/s² — only at Earth's surface, varies with height, depth, latitude, and planet!

Exam Favourite · 2–3 Marks

VARIATION OF g

Master all four cases. This single topic can secure 2–3 NEET marks alone.

g = GM / R²

g at Earth's surface · g = 9.8 m/s² · M = 6×10²⁴ kg · R = 6.4×10⁶ m

g vs r — from Earth's centre to infinity

🏔 With Height (h)

g_h = g(1 − 2h/R) for h ≪ R
g_h = gR²/(R+h)² exact

Inverse-square decrease. Slow at first, faster further out.

⛏ With Depth (d)

g_d = g(1 − d/R)

Linear decrease. At d = R (centre): g = exactly 0. Straight line graph.

🌐 With Latitude (λ)

g_λ = g − Rω²cos²λ

Poles (λ=90°): g is maximum
Equator (λ=0°): g is minimum

🌑 Earth's Shape

Earth is oblate spheroid. R_poles < R_equator. Since g ∝ 1/R², g at poles > g at equator.

💡 Critical Memory Trick:
Height formula: g(1 − 2h/R) → coefficient is 2
Depth formula: g(1 − 1·d/R) → coefficient is 1

For the same small displacement Δ, height reduces g twice as fast as depth! The "2" is the key difference.

🪨 Why is g independent of object's mass?
From F = mg → acceleration a = F/m = mg/m = g. The mass cancels perfectly! A feather and iron ball fall at identical rates in vacuum. Galileo demonstrated this by dropping two different-mass cannonballs from the Leaning Tower of Pisa.

Deep Concept

POTENTIAL & ENERGY

Understanding the negative sign unlocks every energy-based problem in gravitation.

🕳 The Well Analogy: Earth is a deep gravitational well. To escape to infinity, you must climb out — you must add energy. Since we define V = 0 at infinity (the reference), anything closer to Earth has energy less than zero — it is negative. Deeper in the well = more negative = more tightly bound to Earth.

Gravitational Potential (V)

V = −GM/r

Work done per unit mass to bring a test mass from ∞ to point r. Always negative. Unit: J/kg

Gravitational PE (U)

U = −GMm/r

At surface: −GMm/R · At infinity: 0 (reference). Unit: Joule (J)

E_total = −GMm / 2r

KE = +GMm/2r · PE = −GMm/r · Total = −GMm/2r

💡 The Energy Triangle — memorise this:
|KE| = |E_total| = ½|PE|
KE = −(Total Energy) → KE is always positive ✓
PE = 2 × (Total Energy) → PE magnitude is twice total energy ✓
All three are connected by a factor of 2. Never mix their signs!

High Impact · Always in NEET

ESCAPE VELOCITY

The minimum speed to break free from a planet's gravitational grip — forever.

🚀 What is escape velocity?
The minimum launch speed so an object escapes gravity completely — reaching infinity with zero remaining speed. Exactly this speed: just barely makes it out. Any slower: falls back. Any faster: escapes with leftover kinetic energy.

v_e = √(2GM/R) = √(2gR)

Earth: 11.2 km/s · Moon: 2.4 km/s · Sun: 618 km/s · Black hole: > c

Independent of:

✓ Mass of the object (stone or 100-ton rocket — same!)
✓ Direction of launch (vertical or angled — same!)
Only depends on M and R of the planet

By Planet:

Earth: 11.2 km/s
Moon: 2.4 km/s (thin atmosphere!)
Sun: 618 km/s
Black hole: > speed of light!

❌ Classic Mistake

"A heavier rocket needs higher escape velocity to leave Earth."

✅ Correct

v_e = √(2GM/R) has no object mass 'm'. Whether you launch a pebble or a spaceship, escape velocity is the same 11.2 km/s.

💡 The √2 Shortcut:
Given v_o → v_e = v_o × 1.414
Given v_e → v_o = v_e ÷ 1.414

Quick check: v_e = √(2×10×6.4×10⁶) = √(1.28×10⁸) ≈ 11.3 km/s ✓

Scoring Area

SATELLITE MOTION

Orbits, energy, weightlessness, and Kepler's laws — all in one place.

🛰 Why doesn't a satellite fall?
It DOES fall! But it moves sideways so fast that Earth curves away beneath it as fast as it falls. Without gravity it would fly off in a straight line; gravity curves that line into a perfect orbit. The satellite is perpetually missing Earth.

Inside a satellite you float — NOT because gravity is zero (at ISS altitude 400 km, g ≈ 8.7 m/s²!), but because both you and the satellite fall together with identical acceleration. No contact force → no normal reaction → no sensation of weight. Identical to being in a free-falling elevator.

🌐 Geostationary Satellite

T = 24 h (matches Earth's rotation)
Height ≈ 36,000 km above equator
Appears fixed → TV, weather, internet
Must be in equatorial plane only

📡 Polar Satellite

Altitude: 500–800 km · T ≈ 90–100 min
Covers entire Earth surface over time
Used for: mapping, weather, surveillance

💡 Kepler's 3rd Law Application:
T² ∝ r³ → (T₁/T₂)² = (r₁/r₂)³

Double radius → T₂ = 2√2 × T₁ ≈ 2.83×T₁
Quadruple radius → T₂ = 8×T₁

⚠ Exam Danger Zone

COMMON MISTAKES

Seven classic errors that cost students marks every single NEET exam.

❌ Mistake 1

"g and G are the same constant."

✅ Fact

G = 6.67×10⁻¹¹ — universal, never changes. g = 9.8 m/s² only at Earth's surface; varies everywhere.

❌ Mistake 2

"Heavier rocket needs more escape velocity."

✅ Fact

v_e = √(2GM/R) has no object mass! Stone or 100-ton rocket: same 11.2 km/s.

❌ Mistake 3

"Orbital velocity = escape velocity."

✅ Fact

v_e = √2 × v_o. Escape is 41.4% higher than orbital. Critical distinction for MCQs!

❌ Mistake 4

"Satellite potential energy is positive."

✅ Fact

PE = −GMm/r — always negative for bound systems. As r increases, PE approaches 0 from below.

❌ Mistake 5

"g=0 at Earth's centre means no gravity there."

✅ Fact

Gravity exists everywhere. At centre pulls cancel equally from all sides → net g = 0. Two different things!

❌ Mistake 6

"Astronauts float because there's no gravity."

✅ Fact

At ISS (400 km), g ≈ 8.7 m/s² — nearly surface value! They float because both they and the station are in free fall (orbit).

❌ Mistake 7

"Depth reduces g faster than height for same displacement."

✅ Fact

Height: g(1−2h/R). Depth: g(1−d/R). For same Δ, height reduces g twice as fast (coefficient 2 vs 1)!

Rapid Revision

EVERYTHING AT A GLANCE

Read this the night before your exam. Once through. Sleep confident.

All 12 Key Formulas

F = Gm₁m₂/r²

Newton's Law

g = GM/R²

Surface gravity

g_h = g(1−2h/R)

g at height h≪R

g_d = g(1−d/R)

g at depth d

g_λ = g−Rω²cos²λ

g at latitude λ

V = −GM/r

Grav. potential

U = −GMm/r

Gravitational PE

v_e = √(2gR)

Escape velocity

v_o = √(GM/r)

Orbital velocity

v_e = √2 · v_o

Golden relation

T = 2π√(r³/GM)

Time period

E = −GMm/2r

Satellite total E

10 Points you must remember

01G is universal, same everywhere in the cosmos. g varies with location, height, depth, latitude, and planet.
02g is independent of falling object's mass — everything falls at the same rate in vacuum. Mass cancels.
03g = 0 at Earth's centre · g = max at surface · g → 0 at infinity. Two zeros, one maximum.
04Gravitational potential V is always negative. Zero only at infinity (the reference point). Never positive.
05Escape velocity = √2 × orbital velocity. For Earth: 11.2 = 1.414 × 7.9 km/s. Golden rule!
06Satellite: |KE| = |E_total| · |PE| = 2|E_total| · Total E = −GMm/2r (negative = bound to Earth).
07Weightlessness = free fall (orbit), NOT zero gravity. ISS astronauts experience g ≈ 8.7 m/s².
08Geostationary: T = 24 h, h ≈ 36,000 km, equatorial plane only. Polar: T ≈ 90 min, low orbit.
09Height reduces g twice as fast as depth for same small displacement. (Factor 2h/R vs d/R)
10Kepler's 3rd: T²∝r³. Double radius → T×2√2. Quadruple radius → T×8. Always check ratio problems.

🎯 NEET Exam Strategy:
3–5 questions per year from Gravitation. Priority order:
1) Variation of g (height/depth/latitude) — most frequent
2) Escape vs orbital velocity — appears almost every year
3) Satellite energy calculations — direct formula substitution
4) Kepler's law ratios — proportion problems

Practice 1 numerical from each area daily for 7 days = full chapter marks!

🧪 Practice Test

GRAVITATION MCQs

30 exam-standard questions · Instant scoring · Full explanations

⏱ 40 min recommended

📊 NEET pattern

🎯 Score ≥80% = Exam ready

/ 30

Quiz Complete!

See your performance below.

Correct

Wrong

Skipped

Gravitation Complete Master Guide

Mass vs Weight — The #1 Confusion

Why Inverse Square? — Visual Proof

All 12 Key Formulas

Partager :

J’aime ça :

En savoir plus sur eduPhysics

En savoir plus sur eduPhysics