Class 9 Science Chapter 10: Gravitation

Class 9 Science Chapter 10: Gravitation - Complete NCERT Notes

What You'll Master:

✅ Universal Law of Gravitation and its applications
✅ Free fall and acceleration due to gravity
✅ Mass vs Weight (clear distinction)
✅ Thrust and Pressure concepts
✅ Archimedes' Principle and buoyancy
✅ Relative density calculations
✅ Numerical problem-solving techniques
✅ Important derivations for exams

📊 Chapter Overview

Chapter Weightage: 8-10 marks
Difficulty Level: ⚡⚡ Medium-Hard
Expected Questions: 2-3 (1-2 MCQs + 1 Long/Numerical)
Previous Year Frequency: VERY HIGH (Appears every year!)

What Makes This Chapter Special:

Links physics with astronomy
Explains why we don't float away!
Understanding planetary motion
Practical applications everywhere
High numerical problem weightage

🎯 PART 1: INTRODUCTION TO GRAVITATION

What is Gravitation?

Definition:
Gravitation is the force of attraction between any two objects in the universe due to their masses.

Simple Understanding:
Every object in the universe attracts every other object. You attract the Earth, the Earth attracts you, even you and your friend attract each other (though the force is too weak to notice)!

Why Don't We Feel Attraction to Small Objects?

Reason: Gravitational force depends on mass. Small objects have tiny mass, so their gravitational pull is extremely weak.

Example:

Earth's mass = 6 × 10²⁴ kg → Strong pull (we feel it!)
Your friend's mass = 50 kg → Negligible pull (can't feel it!)

🌍 PART 2: UNIVERSAL LAW OF GRAVITATION

Newton's Universal Law of Gravitation

Statement:
Every object in the universe attracts every other object with a force which is:

Directly proportional to the product of their masses
Inversely proportional to the square of the distance between them

The Formula:

F = G × (m₁ × m₂) / d²

Where:

F = Gravitational force (in Newtons, N)
G = Universal gravitational constant = 6.67 × 10⁻¹¹ N m²/kg²
m₁ = Mass of first object (in kg)
m₂ = Mass of second object (in kg)
d = Distance between centers of objects (in meters)

Memory Trick: "FGM²D²"

Force equals G times Mass squared over Distance squared

🧒 ELI5: Universal Law of Gravitation

Imagine you and your friend are magnets:

Think of gravity like invisible rubber bands connecting everything in the universe!

The heavier you both are → Stronger the rubber band pulls you together
The farther apart you are → Weaker the rubber band becomes

Real Example:

If you double your mass → Force doubles! ✅
If you double the distance → Force becomes 1/4 (because of d²)! ✅

Why don't you feel pulled to your friend?
Because you're both too light compared to Earth! It's like trying to hear a whisper during a rock concert - Earth's "shout" drowns it out!

Remember: Gravity never pushes - it ONLY pulls! Always attraction, never repulsion! 🧲

Importance of Universal Law

1. Explains Planetary Motion

Why planets orbit the Sun
Why Moon orbits Earth
How satellites stay in orbit

2. Explains Tides

Ocean tides due to Moon's gravity
High tide and low tide patterns

3. Explains Our Weight

Why we stick to Earth's surface
Why astronauts float in space

4. Universal Application

Works for atoms, apples, planets, galaxies!
Same law throughout the universe

📐 PART 3: GRAVITY AND ACCELERATION DUE TO GRAVITY

What is Gravity?

Definition:
The force of attraction exerted by Earth on any object is called gravity.

Note: Gravity is a special case of gravitation (specifically Earth's gravitational force)

Acceleration Due to Gravity (g)

Definition:
The acceleration produced in a freely falling body due to Earth's gravitational force is called acceleration due to gravity.

Symbol: g
Value on Earth's surface: 9.8 m/s² (approximately 10 m/s² for calculations)

Formula for 'g':

g = G × M / R²

Where:

G = 6.67 × 10⁻¹¹ N m²/kg²
M = Mass of Earth = 6 × 10²⁴ kg
R = Radius of Earth = 6.4 × 10⁶ m

Calculation: g = (6.67 × 10⁻¹¹ × 6 × 10²⁴) / (6.4 × 10⁶)²
g = 9.8 m/s²

🧒 ELI5: What is 'g' Really?

Imagine Earth is a giant vacuum cleaner:

Every second, it makes you fall faster by 9.8 m/s!

What this means:

After 1 second: You're falling at 9.8 m/s
After 2 seconds: You're falling at 19.6 m/s (9.8 + 9.8)
After 3 seconds: You're falling at 29.4 m/s (9.8 + 9.8 + 9.8)

Why same for feather and stone?
In vacuum (no air), they both accelerate at same rate! Air resistance makes feather fall slowly, not gravity!

Fun Fact: On the Moon, g = 1.6 m/s² (1/6th of Earth). That's why astronauts can jump so high! 🌙

Factors Affecting 'g'

1. Altitude (Height Above Earth)

Formula: g' = g × [R² / (R + h)²]

Where:

g' = gravity at height h
R = radius of Earth
h = height above surface

Effect: g decreases with altitude

Example: On mountains, you weigh slightly less!

2. Depth (Below Earth's Surface)

Formula: g' = g × (1 - d/R)

Where:

d = depth below surface

Effect: g decreases with depth

At Earth's center: g = 0 (weightless!)

3. Shape of Earth

Earth is not a perfect sphere (bulges at equator)
g is maximum at poles
g is minimum at equator

Values:

At poles: g = 9.83 m/s²
At equator: g = 9.78 m/s²

🪂 PART 4: FREE FALL

What is Free Fall?

Definition:
When an object falls towards Earth under the influence of gravitational force alone (with no other forces acting), it is said to be in free fall.

Conditions for Free Fall:

Only gravity acts on the object
No air resistance
No other external forces

Important: In real life, air resistance exists, so true free fall is rare (happens in vacuum)

Equations of Motion for Free Fall

Since acceleration is constant (g), we use equations of motion:

1. v = u + gt

v = final velocity
u = initial velocity
g = 9.8 m/s²
t = time

2. s = ut + ½gt²

s = distance fallen

3. v² = u² + 2gs

For Objects Dropped from Rest:

u = 0
So equations become:
- v = gt
- s = ½gt²
- v² = 2gs

🎯 Numerical Problems Strategy

Example Problem:
A stone is dropped from a height of 80m. Calculate: (a) Time taken to reach ground (b) Final velocity when it hits ground (Take g = 10 m/s²)

Solution:

Given:

u = 0 (dropped, not thrown)
s = 80 m
g = 10 m/s²

(a) Time taken:

Using s = ut + ½gt²

80 = 0 × t + ½ × 10 × t²
80 = 5t²
t² = 16
t = 4 seconds ✅

(b) Final velocity:

Using v = u + gt

v = 0 + 10 × 4
v = 40 m/s ✅

Alternate method for (b):

Using v² = u² + 2gs

v² = 0 + 2 × 10 × 80
v² = 1600
v = 40 m/s ✅

Common Mistakes in Free Fall Problems ❌

Mistake 1: Forgetting u = 0 when object is dropped
Correct: Dropped means u = 0, thrown means u ≠ 0

Mistake 2: Using wrong sign for g
Correct:

Falling down → g is positive (+9.8)
Thrown up → g is negative (-9.8)

Mistake 3: Not converting units
Correct: Always convert km → m, minutes → seconds

⚖️ PART 5: MASS AND WEIGHT

Mass

Definition:
The amount of matter contained in an object is called its mass.

Properties:

Scalar quantity
Measured in kilograms (kg)
Constant everywhere (same on Earth, Moon, space!)
Measured by beam balance

Formula: Mass has no formula (it's a fundamental quantity)

Weight

Definition:
The force with which Earth attracts an object is called weight.

Properties:

Vector quantity (has direction - towards Earth's center)
Measured in Newtons (N)
Changes with location (different on Earth, Moon, space!)
Measured by spring balance

Formula:

W = m × g

Where:

W = Weight (in N)
m = Mass (in kg)
g = Acceleration due to gravity (9.8 m/s² on Earth)

🧒 ELI5: Mass vs Weight

Mass = How much "stuff" you're made of
Think of it like the number of LEGO bricks you used to build yourself. Same number of bricks whether you're on Earth or Moon!

Weight = How hard gravity pulls you
On Earth: Strong pull (you weigh 60 kg)
On Moon: Weak pull (you weigh 10 kg)
In space: No pull (you weigh 0 kg - weightless!)

BUT - You're still made of the same LEGO bricks (mass stays same)!

Real Example:

Your mass = 50 kg (everywhere!)
Your weight on Earth = 50 × 9.8 = 490 N
Your weight on Moon = 50 × 1.6 = 80 N
Your weight in space = 0 N (floating!)

Memory Trick:
Mass is Matter (same everywhere)
Weight Wanders (changes with place)

Comparison Table: Mass vs Weight

Property	Mass	Weight
Definition	Amount of matter	Force of gravity
Type	Scalar	Vector
Unit	kg	N (Newton)
Depends on	Nothing!	Gravity (g)
Value on Earth	50 kg	490 N
Value on Moon	50 kg	80 N
Value in space	50 kg	0 N
Measured by	Beam balance	Spring balance
Formula	-	W = mg

Weight on Different Celestial Bodies

Formula: W = m × g

Location	g (m/s²)	Weight of 60 kg person
Earth	9.8	588 N
Moon	1.6	96 N (1/6 of Earth)
Mars	3.7	222 N
Jupiter	25	1500 N (2.5× Earth!)
Sun	274	16,440 N (28× Earth!)

Important: Mass remains 60 kg everywhere!

💪 PART 6: THRUST AND PRESSURE

Thrust

Definition:
The force acting perpendicular to a surface is called thrust.

Properties:

It's a force
Acts perpendicular (90°) to surface
Measured in Newtons (N)

Example:
When you stand on sand, your feet exert thrust (downward force) on sand.

Pressure

Definition:
The force acting per unit area of a surface is called pressure.

Formula:

Pressure = Thrust / Area

P = F / A

Where:

P = Pressure (in Pascal, Pa)
F = Force/Thrust (in N)
A = Area (in m²)

SI Unit: Pascal (Pa)
1 Pascal = 1 N/m²

Other units:

1 atm = 10⁵ Pa (atmospheric pressure)
1 bar = 10⁵ Pa

🧒 ELI5: Thrust vs Pressure

Thrust = How hard you push
Pressure = How hard you push PER SQUARE INCH

Imagine walking on snow:

Wearing normal shoes:

Your weight (thrust) = 500 N
Shoe area = Small
Pressure = High
Result: You sink! ❌

Wearing snowshoes:

Your weight (thrust) = 500 N (same!)
Shoe area = Large
Pressure = Low
Result: You don't sink! ✅

Same thrust, different pressure!

Memory Trick:
Think of a thumbtack: Sharp point = Small area = High pressure = Goes through easily!

Applications of Pressure

1. Sharp Knife Cuts Better

Small area → High pressure → Easy cutting

2. Broad Straps on School Bags

Large area → Low pressure → Less pain on shoulders

3. Nail Has Sharp Point

Small area → High pressure → Penetrates easily

4. Foundations Are Broad

Large area → Low pressure → Building doesn't sink

5. Camel's Feet Are Broad

Large area → Low pressure → Doesn't sink in sand

Numerical Problem Example:

Question:
A force of 200 N acts on an area of 0.5 m². Calculate the pressure.

Solution:

Given:

F = 200 N
A = 0.5 m²

Using P = F/A

P = 200 / 0.5
P = 400 Pa ✅

🌊 PART 7: PRESSURE IN FLUIDS

What are Fluids?

Definition:
Substances that can flow are called fluids.

Examples: Liquids and gases

Properties:

Take shape of container
Exert pressure in all directions
Pressure increases with depth

Pressure Due to a Liquid Column

Formula:

P = h × ρ × g

Where:

P = Pressure (Pa)
h = Height/Depth of liquid column (m)
ρ (rho) = Density of liquid (kg/m³)
g = 9.8 m/s²

Important Points:

Pressure increases with depth
Pressure at same depth is same in all directions
Pressure depends on density of liquid

Why dams are thicker at bottom?
Because water pressure is maximum at bottom!

Atmospheric Pressure

Definition:
The pressure exerted by air column in atmosphere is called atmospheric pressure.

Value at sea level: 1 atm = 1.01 × 10⁵ Pa

Why don't we feel it?
Because our body fluids exert equal pressure outward, balancing it!

Experiment: Crushing can experiment - When air inside is removed, atmospheric pressure crushes the can!

🛟 PART 8: BUOYANCY AND ARCHIMEDES' PRINCIPLE

Buoyancy

Definition:
The upward force exerted by a fluid on an object immersed in it is called buoyant force or upthrust.

Why does it occur?
Because pressure increases with depth. Bottom of object experiences more pressure than top, creating net upward force!

Archimedes' Principle

Statement:
When a body is immersed fully or partially in a fluid, it experiences an upward force (buoyant force) equal to the weight of the fluid displaced by it.

Formula:

Buoyant Force = Weight of fluid displaced

F_b = V × ρ × g

Where:

V = Volume of object immersed
ρ = Density of fluid
g = 9.8 m/s²

🧒 ELI5: Archimedes' Principle

Imagine a bathtub filled to the brim:

When you sit in it, water overflows, right?

That overflowed water = Fluid displaced
Weight of that water = Buoyant force pushing you up!

Real-Life Examples:

1. Swimming Pool:

You displace water
Water pushes you up
You feel lighter!

2. Ship Floats:

Huge ship displaces tons of water
Buoyant force = Weight of displaced water
Supports the ship!

3. Iron Nail Sinks, Ship Floats (Both Iron!):

Nail: Displaces little water → Small buoyant force → Sinks
Ship: Hollow, displaces lots of water → Large buoyant force → Floats!

Memory Trick: "EUREKA!"
That's what Archimedes shouted when he discovered this in his bathtub! 🛁

Objects in Fluids: Three Cases

Case 1: Object Floats

Buoyant force > Weight of object
Example: Wood in water, boat

Case 2: Object Sinks

Buoyant force < Weight of object
Example: Iron nail in water

Case 3: Object Stays Suspended

Buoyant force = Weight of object
Example: Submarine underwater

📊 PART 9: RELATIVE DENSITY

What is Relative Density?

Definition:
The ratio of density of a substance to the density of water at 4°C is called relative density.

Formula:

Relative Density = Density of substance / Density of water

R.D. = ρ_substance / ρ_water

Important: Relative density has no unit (it's a ratio)

Density of water at 4°C = 1000 kg/m³ = 1 g/cm³

Alternative Formula:

Relative Density = Mass of substance / Mass of equal volume of water

Examples:

Substance	Density (kg/m³)	Relative Density
Water	1000	1
Ice	900	0.9
Iron	7800	7.8
Mercury	13600	13.6
Gold	19300	19.3

Interpretation:

R.D. = 7.8 means iron is 7.8 times denser than water
R.D. = 0.9 means ice is 0.9 times (lighter than) water

🧮 PART 10: IMPORTANT NUMERICAL PROBLEMS

Problem 1: Gravitational Force

Question:
Two objects of mass 10 kg and 20 kg are separated by 2 m. Calculate the gravitational force between them.
(G = 6.67 × 10⁻¹¹ N m²/kg²)

Solution:

Given:

m₁ = 10 kg
m₂ = 20 kg
d = 2 m
G = 6.67 × 10⁻¹¹ N m²/kg²

Using F = G × (m₁ × m₂) / d²

F = (6.67 × 10⁻¹¹ × 10 × 20) / (2)²
F = (6.67 × 10⁻¹¹ × 200) / 4
F = 1334 × 10⁻¹¹ / 4
F = 333.5 × 10⁻¹¹
F = 3.335 × 10⁻⁹ N ✅

Problem 2: Acceleration Due to Gravity

Question:
Calculate the value of 'g' on Moon if its mass is 7.4 × 10²² kg and radius is 1.74 × 10⁶ m.
(G = 6.67 × 10⁻¹¹ N m²/kg²)

Solution:

Given:

M = 7.4 × 10²² kg
R = 1.74 × 10⁶ m
G = 6.67 × 10⁻¹¹ N m²/kg²

Using g = G × M / R²

g = (6.67 × 10⁻¹¹ × 7.4 × 10²²) / (1.74 × 10⁶)²
g = (49.358 × 10¹¹) / (3.0276 × 10¹²)
g = 49.358 / 30.276
g = 1.63 m/s² ≈ 1.6 m/s² ✅

Problem 3: Mass and Weight

Question:
An object weighs 50 N on Earth. What will be its: (a) Mass on Earth (b) Weight on Moon (g_moon = 1.6 m/s²)

Solution:

(a) Mass on Earth:

Using W = m × g

50 = m × 9.8
m = 50 / 9.8
m = 5.1 kg ✅

(b) Weight on Moon:

W_moon = m × g_moon
W_moon = 5.1 × 1.6
W_moon = 8.16 N ✅

Note: Mass remains same (5.1 kg) on Moon!

Problem 4: Pressure

Question:
A brick of dimensions 20 cm × 10 cm × 5 cm weighs 10 N. Calculate: (a) Maximum pressure (b) Minimum pressure

Solution:

Areas of three faces:

Face 1: 20 × 10 = 200 cm² = 0.02 m²
Face 2: 20 × 5 = 100 cm² = 0.01 m² (smallest)
Face 3: 10 × 5 = 50 cm² = 0.005 m²

(a) Maximum pressure (when smallest area in contact):

P_max = F / A_min
P_max = 10 / 0.005
P_max = 2000 Pa ✅

(b) Minimum pressure (when largest area in contact):

P_min = F / A_max
P_min = 10 / 0.02
P_min = 500 Pa ✅

Problem 5: Relative Density

Question:
A piece of metal weighs 200 g in air and 180 g when fully immersed in water. Calculate its relative density.

Solution:

Weight in air = 200 g
Weight in water = 180 g

Loss in weight = Weight in air - Weight in water
Loss = 200 - 180 = 20 g

This loss = Weight of water displaced

Relative Density = Weight in air / Loss in weight
R.D. = 200 / 20
R.D. = 10 ✅

This means the metal is 10 times denser than water!

📝 PART 11: PREVIOUS YEAR QUESTIONS ANALYSIS

Pattern Observed:

MCQs (1 mark each):

Formula-based: Direct substitution
Conceptual: Mass vs weight, free fall
Application: Why knife is sharp, etc.

Short Answer (2-3 marks):

Derivations: g = GM/R²
Numerical: Simple calculations
Define and explain: Buoyancy, thrust

Long Answer (5 marks):

Numerical problems (2-3 steps)
Archimedes' principle + application
Mass vs weight with examples

Most Frequently Asked:

Calculate gravitational force (every year!)
Mass and weight difference
Archimedes' principle statement
Why value of g decreases with altitude
Pressure numerical problems

🎯 PART 12: EXAM STRATEGY

How to Score Full Marks

For MCQs:

✅ Remember all formulas
✅ Know units of all quantities
✅ Practice quick mental calculations
✅ Understand concept, don't just memorize

For Numericals:

✅ Always write:

Given (what's provided)
To find (what's asked)
Formula
Substitution
Answer with unit

✅ Check:

Units are consistent (convert if needed)
Final answer has correct unit
Rounding off (2 decimal places usually)

For Theory Questions:

✅ Start with definition
✅ Give formula if applicable
✅ Add diagram if helps
✅ Give 2-3 examples
✅ Conclude properly

Memory Tricks for Formulas

"FGM²D²" - Gravitational Force
F = G × M₁M₂ / D²

"GMOR²" - Acceleration due to gravity
g = G × M / R²

"WiMG" - Weight is Mass times Gravity
W = m × g

"PROAG" - Pressure
P = ρ × h × g (for liquids)
P = F / A (general)

"Very Romantic Guy" - Relative Density
R.D. = Density of substance / Density of water

🚀 PART 13: QUICK REVISION CHECKLIST

Formulas to Remember:

F = G × (m₁ × m₂) / d²
g = G × M / R²
W = m × g
P = F / A
P = h × ρ × g
Buoyant force = V × ρ × g
R.D. = ρ_substance / ρ_water
v = u + gt
s = ut + ½gt²
v² = u² + 2gs

Constants to Remember:

G = 6.67 × 10⁻¹¹ N m²/kg²
g (Earth) = 9.8 m/s²
g (Moon) = 1.6 m/s²
Density of water = 1000 kg/m³
1 atm = 1.01 × 10⁵ Pa

Key Concepts:

Gravitation is universal (works everywhere)
Mass is constant, weight changes
g decreases with altitude and depth
Pressure increases with depth in liquids
Buoyant force = Weight of displaced fluid
Relative density has no unit

❓ PART 14: PRACTICE QUESTIONS

Section A: MCQs (1 mark each)

Q1. The value of G is: (a) 9.8 N/kg (b) 6.67 × 10⁻¹¹ N m²/kg² ✅ (c) 10 m/s² (d) Variable

Q2. SI unit of pressure is: (a) N (b) Pascal ✅ (c) kg/m² (d) N/kg

Q3. On which principle does a hydraulic lift work? (a) Newton's law (b) Archimedes' principle ✅ (c) Bernoulli's theorem (d) Pascal's law

Q4. If mass of an object is 10 kg on Earth, what will be its mass on Moon? (a) 60 kg (b) 1.67 kg (c) 10 kg ✅ (d) 0 kg

Q5. Acceleration due to gravity is maximum at: (a) Equator (b) Poles ✅ (c) Mountains (d) Same everywhere

Section B: Short Answer (2-3 marks each)

Q6. State the universal law of gravitation and write its formula.

Q7. Why is it easier to swim in sea water than in river water?

Q8. Differentiate between mass and weight with 3 points.

Q9. A stone is dropped from a tower of height 80 m. Calculate its velocity when it reaches the ground. (g = 10 m/s²)

Q10. Why do we feel lighter when we swim?

Section C: Long Answer (5 marks each)

Q11. (a) State Archimedes' principle. (b) Why does an iron nail sink while a ship made of iron floats? (c) Give two applications of Archimedes' principle.

Q12.
Two objects A and B have masses 5 kg and 10 kg respectively. They are separated by 3 m. (a) Calculate the gravitational force between them. (b) If distance is doubled, what happens to the force? (c) If mass of A is doubled, what happens to the force?

Q13.
(a) Derive the expression for acceleration due to gravity (g = GM/R²). (b) Why does value of g decrease with: (i) Altitude (ii) Depth

💡 PART 15: FUN FACTS & TRIVIA

Did You Know?

🌍 Your weight changes throughout the day!
You weigh slightly less on mountains because g decreases with altitude!

🌙 Astronauts on Moon:
Can jump 6 times higher than on Earth because g is 1/6th!

🏊 Dead Sea Mystery:
You float easily because water is very dense (high salt content) → More buoyant force!

⚖️ Weightless in Space:
Not because there's no gravity, but because you're in continuous free fall!

🎈 Why balloons float:
Helium is less dense than air → Buoyant force > Weight → Floats up!

🐫 Camel's wide feet:
Large area → Low pressure → Doesn't sink in sand!

🏆 PART 16: TOPPER'S STRATEGY

How 95%+ Scorers Study Gravitation:

Week 1: Concept Building

Read NCERT thoroughly
Understand each formula derivation
Make formula chart

Week 2: Practice

Solve NCERT exercises
Attempt numericals (at least 20)
Time yourself

Week 3: Revision

Revise formulas daily
Solve previous year papers
Identify weak areas

Last Week Before Exam:

Quick revision of formulas
Practice only numericals
Revise common mistakes

Time Management in Exam:

MCQs: 30 seconds each
2-mark questions: 2-3 minutes
3-mark questions: 4-5 minutes
5-mark numericals: 6-7 minutes

Common Mistakes to Avoid:

❌ Forgetting to convert units (cm → m)
❌ Not writing formula before substitution
❌ Missing units in final answer
❌ Confusing mass and weight
❌ Wrong signs in equations of motion

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🎓 FINAL WORDS

Gravitation is not just formulas and calculations - it's the force that keeps the universe together! From keeping you on Earth to holding planets in orbit, gravity is everywhere.

Target for This Chapter:
✅ Score 8-9 out of 10 marks
✅ Master all numericals
✅ Clear concepts for Class 11 Physics

Remember:

Practice numericals daily
Understand concepts, don't just memorize
Relate to real-life examples
Revise formulas regularly

You've got this! 💪🚀

Last Updated: February 2025
Aligned With: Latest CBSE Syllabus 2024-25
Total Pages: 18+ pages of comprehensive notes
Question Bank: 13 practice questions included

Created with 💙 by NCERT Nation Team

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