Gravitation Class 9 Science Revision Notes

Gravitation Class 9 Science Notes: Gravitation Class 9 Science Notes help students understand one of the most important concepts in physics – the force that attracts objects towards each other. From the falling of an apple to the movement of planets around the Sun, gravitation plays a major role in our daily life and in the universe. In this chapter, students learn about gravitational force, universal law of gravitation, mass, weight, free fall, and thrust and pressure in a simple and practical way.

These gravitation class 9 notes are prepared according to the latest syllabus and explain every topic using easy language, examples, formulas, and important concepts. Students can use these notes for quick revision before exams and to strengthen their understanding of fundamental physics principles. The chapter also explains how gravity affects objects on Earth and why celestial bodies remain in their orbits.

For better learning, many students prefer gravitation class 9 science notes with diagram, as diagrams make concepts like free fall and gravitational attraction easier to visualize and remember. If you are looking for a quick revision resource, gravitation class 9 science notes pdf can be very useful for studying anytime and anywhere.

Why Does an Apple Fall?

When Sir Isaac Newton observed an apple fall from a tree, he asked a profound question: Why does the apple fall down, but the Moon doesn't? His insight was revolutionary the same force that pulls the apple toward Earth also keeps the Moon in orbit. He proposed that every object in the universe attracts every other object with a force called gravitation.

This single idea the Universal Law of Gravitation unified terrestrial and celestial mechanics for the first time in human history.

Gravitation vs Gravity – A Crucial Distinction

Forces of gravitation between everyday objects are extremely weak; forces of gravity (involving planets) are massive.

2. Newton's Universal Law of Gravitation

Every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The force acts along the line joining the centres of the two particles.

Mathematical Form

Let two particles of masses m₁ and m₂ be separated by a distance r. Then:

F ∝ m₁m₂ and F ∝ 1/r₂

Combining these:

F = G⋅m₁m₂/r₂

Where G is the Universal Gravitational Constant.

Universal Gravitational Constant (G)

G is numerically equal to the force of gravitational attraction between two bodies of unit mass each, kept at a unit distance apart.

(From F = Gm₁m₂/r² : if m₁ = m₂ = 1 and r = 1, then F = G.)

Value and Units of G

The extremely small value of G explains why we don't feel any noticeable attraction between everyday objects around us even though gravitational force is always acting between them.

Important Characteristics of Gravitational Force

1. It is always an attractive force; never repulsive.
2. It forms an action–reaction pair equal in magnitude, opposite in direction (Newton's Third Law).
3. It is a central force acts along the line joining the centres of the two bodies.
4. It is independent of the intervening medium (works equally well through air, water, or vacuum).
5. It is independent of the presence of other bodies.
6. It is a long-range force acts even across enormous astronomical distances (e.g., between the Sun and Earth, separated by 1.5 × 10⁸ km).
7. It is a conservative force work done depends only on the initial and final positions, not the path.
8. Gravitational force is negligible for light bodies but becomes enormous for massive bodies like stars and planets.

Experimental Evidence for Newton's Law

• Planets orbit the Sun because of the gravitational force between the Sun and each planet.
• Ocean tides are caused mainly by the Moon's gravitational pull on Earth's water bodies.
• Satellites orbit planets due to gravitational force.
• Earth's atmosphere is retained because of Earth's gravity.

Newton's Third Law and Gravitation Why Doesn't Earth Rise to Meet the Falling Apple?

When a stone is dropped, Earth pulls the stone with a force F and the stone pulls Earth with the same force F (Newton's Third Law). Then why don't we see Earth rising up toward the stone?

The answer lies in Newton's Second Law: a = F / m.

• The stone has a tiny mass → produces a large acceleration (≈ 9.8 m/s²) → it visibly falls.
• Earth has a gigantic mass (≈ 6 × 10²⁴ kg) → produces a vanishingly small acceleration → far too small to observe.

Both are attracting each other equally but the visible motion belongs to whichever has less mass.

Solved Examples on Gravitational Force

Example 1 – Force Between Two People

Q. Two persons of mass 50 kg each stand 1 m apart. Find (a) the gravitational force between them and (b) the force of gravity each experiences from Earth. (Mass of Earth = 6 × 10²⁴ kg, Radius = 6.4 × 10⁶ m)

Solution:

(a) Force between the persons:

F = Gm₁m₂/r² = 6.67 x 10^-11 x 50 x 50/1² = 1.67 x 10^-7 N

(b) Force of gravity from Earth on each person:

F' = G.M_Earth .m/R² = 6.67 X 10^-11 x 6 x 10²⁴ x 50/(6.4 x 10⁶)² ≈ 480 N

Conclusion: Earth's pull on each person (≈480 N) is roughly 3 billion times stronger than their mutual attraction which is why they don't drift toward each other.

Example 2 – Balancing Gravitational Forces

Q. Two bodies A (mass m) and B (mass 2m) are placed a distance d apart. Where should a small particle be placed on the line AB so that the net gravitational force on it is zero?

Solution:

Let the particle be at distance x from A. For zero net force, force from A = force from B:

Gm/x2 = G(2m)/(d -x)2

(d -x)² = 2x² ⇒ d - x = √2.x

x = d/1 + √2

The particle must be placed closer to the lighter body A at a distance d/(1 + √2) ≈ 0.414d from A.

Equations of Motion for Freely Falling Bodies

Since g is constant near Earth's surface, the three kinematic equations apply just replace a → g and s → h:

Sign Conventions

• g is positive when motion is downward (same direction as g).
• g is negative when motion is upward (opposite to g).
• Upward distance/velocity is positive; downward is negative.

Points to Remember

1. A body dropped freely has initial velocity u = 0.
2. A body thrown straight up has final velocity v = 0 at the highest point.
3. Time to rise = time to fall for the same height.
4. Distance fallen ∝ (time)² a freely falling body covers far more distance in later seconds.

Mass vs Weight – The Most Tested Distinction

Why Weight Changes with Location

Weight, W = m × g. Since mass is constant, only g changes:

• At Poles: g is maximum → weight is maximum.
• At Equator: g is slightly less → weight is slightly less.
• At High Altitude (e.g., Mount Everest): g decreases → weight decreases.
• Going Underground: g decreases → weight decreases.
• At Earth's Centre: g = 0 → weight = 0.

Weight on the Moon

Since g_moon ≈ g_earth / 6:

W_moon = 1/6 W_earth

A 60 kg person who weighs 588 N on Earth would weigh only about 98 N on the Moon though their mass is still 60 kg.

Why "kg-wt" is a Unit of Force

A 1 kg mass on Earth experiences a force of W = 1 × 9.8 = 9.8 N. Hence:

1 kg-wt=9.8 N

Difference Between 'g' and 'G' (Frequently Asked in Exams)

Weightlessness – The Floating Astronaut

What is Weightlessness?

Weightlessness is the condition in which a body experiences zero apparent weight usually because it is in a state of free fall.

A weighing machine measures reaction force, not actual gravitational pull. When you stand on it, your weight compresses the spring, and the upward reaction registers as your weight.

But in a free fall, there's nothing to push back there's no reaction. The pointer reads zero, even though gravity is still acting.

Demonstration

Hang a stone from a spring balance held in your hand it shows the stone's weight. Now drop the entire setup (spring balance + stone). During the fall, both fall together with the same acceleration g, so the spring isn't stretched at all, and the balance reads zero.

Astronauts in a Satellite – Why They Float

A satellite (and everything inside it) is in continuous free fall around Earth but it never hits Earth because of its horizontal velocity. Inside, both the astronaut and the spacecraft accelerate at the same rate g. The astronaut exerts no force on the floor, the floor exerts no force on the astronaut and so the astronaut floats.

Important: The astronaut is not in zero gravity gravity is still pulling them. They are in free fall, which produces apparent weightlessness.

FLUIDS, PRESSURE, AND BUOYANCY

What is a Fluid?

A fluid is any substance that flows under an applied force and takes the shape of its container. Liquids and gases are both fluids.

• Study of fluids at rest → Hydrostatics / Fluid Statics
• Study of fluids in motion → Hydrodynamics

This chapter focuses on liquids at rest.

Thrust and Pressure

Thrust

The total force exerted by a fluid perpendicular to the surface in contact with it is called thrust.

• Thrust is a force → SI unit: newton (N).

Pressure

Pressure is the force (thrust) acting per unit area, applied perpendicular to the surface.

P = F/A

• Pressure is a scalar quantity (hydrostatic pressure acts equally in all directions at a point).
• SI Unit: Pascal (Pa) = N/m²
• CGS Unit: dyne/cm²
• 1 atm = 1.013 × 10⁵ Pa (atmospheric pressure at sea level)

The unit Pascal honours Blaise Pascal, the French scientist who pioneered fluid pressure studies.

Pressure Exerted by a Liquid Column

Consider a liquid of density ρ filled in a cylindrical vessel of cross-sectional area A up to a height h.

• Volume of liquid = A × h
• Mass of liquid = A × h × ρ
• Weight (thrust on base) = A × h × ρ × g
• Pressure on the base:

P = hρg

Important properties:

• Liquid pressure depends only on depth, density, and g not on the shape of the container.
• At a depth h below an open liquid surface, total pressure = atmospheric pressure + hρg.
• Pressure acts equally in all directions at a given depth.

Real-Life Applications of Pressure

Why Pressure Should Be Increased

Why Pressure Should Be Reduced

Buoyancy and the Buoyant Force (Upthrust)

The Observation

• A bucket of water feels lighter while still inside a well but feels heavy the moment it leaves the water surface.
• A heavy iron anchor feels lighter underwater.

Definition

When a body is immersed (partially or fully) in a fluid, the fluid exerts an upward force on the body. This force is called the buoyant force (or upthrust), and the phenomenon is called buoyancy.

Factors Affecting Buoyant Force

The buoyant force depends on:

1. Volume of the body immersed in the fluid (larger immersed volume → larger upthrust).
2. Density of the fluid (denser fluid → larger upthrust).

It does NOT depend on the mass of the body or the depth at which it is submerged.

Demonstration: A wooden block rises faster in salt water (denser) than in fresh water proving buoyant force increases with fluid density.

Archimedes' Principle

The Greek mathematician Archimedes of Syracuse (3rd century BCE) is said to have leapt from his bath shouting "Eureka!" upon discovering this principle.

Statement

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

Mathematical Derivation

Consider a cylindrical body of cross-sectional area a submerged in a liquid of density ρ. Let the top face be at depth h₁ and the bottom face at depth h₂ below the surface.

• Downward thrust on top: F₁ = h₁ ρ g × a
• Upward thrust on bottom: F₂ = h₂ ρ g × a

The horizontal thrusts on the vertical sides cancel out.

Net upward (buoyant) force:

F = F₂ − F₁ = (h₂ − h₁)ρg⋅a = Vρg

where V = (h₂ − h₁) × a is the volume of the immersed body = volume of displaced liquid.

F_buoyant = Vρg = Weight of fluid displaced

Applications of Archimedes' Principle

Archimedes' Principle is used to design:

• Ships and submarines (which displace enough water to float despite being made of steel)
• Hydrometers instruments for measuring liquid densities
• Lactometers used to test the purity of milk
• Hot-air balloons buoyant force from displaced cool air lifts them

Density and Relative Density

Density (ρ)

Density is mass per unit volume.

ρ=M/V

• SI Unit: kg/m³
• CGS Unit: g/cm³

Relative Density (RD) / Specific Gravity

Relative density is the ratio of the density of a substance to the density of water at 4°C.

R.D. =ρ_substance/ρ_water at 4°C

• Relative density is a pure number with no units.
• It tells how many times a substance is heavier (or lighter) than an equal volume of water.

Table of Densities and Relative Densities

Physical meaning: A relative density of 10.5 (for silver) means silver is 10.5 times heavier than an equal volume of water.

Measuring Relative Density Using Archimedes' Principle

For Solids:

R.D. = Weight of body in air/Loss in weight when fully immersed in water = W₁/W₁−W₂

For Liquids:

R.D. = Loss in weight in liquid/Loss in weight in water = W − W′′/W−W′ 

where W = weight in air, W′ = weight in water, W″ = weight in liquid.

Law of Floatation

When a body is immersed in a fluid, two forces act on it:

1. Weight (W) acting downward through the centre of gravity.
2. Buoyant force (B) acting upward through the centre of buoyancy.

Three cases arise:

Statement of Law of Floatation

A body floats in a fluid if the weight of the fluid displaced by the immersed part of the body equals the weight of the body.

Relation Between Densities for a Floating Body

Let ρ₁ = density of solid, V₁ = total volume of solid, ρ₂ = density of liquid, V₂ = volume of solid immersed.

Weight of solid = Weight of liquid displaced:

V₁ρ₁g = V₂ρ₂g

ρ₁/ρ₂ = V₂V₁ = Fraction of volume immersed

Example: Ice has density 920 kg/m³, water has 1000 kg/m³. So fraction of iceberg immersed = 920/1000 = 0.92. Hence only 8% of an iceberg is visible above water the famous "tip of the iceberg."

Conditions for Stable Equilibrium of a Floating Body

1. Weight of body = weight of liquid displaced.
2. Centre of gravity (G) and centre of buoyancy (B) lie on the same vertical line.
3. Stable equilibrium: G lies vertically above B (so that any tilt creates a restoring torque). This is why ships are designed with low centres of gravity.

Important Note-Melting Ice in Water

When an ice block floating in water melts completely, the water level remains unchanged (the volume of water it displaced exactly equals the volume of water it produces on melting).

If ice is floating in a denser liquid (e.g., brine), the water level rises on melting. If ice is floating in a lighter liquid (e.g., alcohol), the level falls.