Class 9 Science – Chapter: Gravitation Notes
✨ Introduction to Gravitation
Gravitation is the force of attraction between any two objects in the universe due to their masses.
It is a universal force acting at a distance.
Example: A fruit falling from a tree, Earth revolving around the Sun.
🔹 Universal Law of Gravitation
Statement: Every object in the universe attracts every other object with a force:
Directly proportional to the product of their masses.
Inversely proportional to the square of the distance between them.
Formula:
F = G × (m₁ × m₂) / r²
Where:
F = Gravitational force
G = Universal gravitational constant (6.674 × 10⁻¹¹ Nm²/kg²)
m₁, m₂ = Masses of the two objects
r = Distance between the centers of the two objects
Example: The gravitational force between Earth and Moon keeps the Moon in orbit.
🔹 Importance of the Law
Explains motion of planets, satellites.
Helps calculate weight, orbits, tides.
| Quantity | SI Unit | Nature |
|---|---|---|
| Force | Newton (N) | Vector |
| G | Nm²/kg² | Constant (Universal) |
🔹 Free Fall
When an object falls under the influence of gravity alone, it is said to be in free fall.
Acceleration due to gravity is denoted by g.
Formula:
F = m × g
g ≈ 9.8 m/s² (on Earth)
Example: A stone dropped from a roof accelerates downward due to gravity.
🔹 Acceleration Due to Gravity (g)
Derived from Newton’s law:
Formula:
g = G × M / R²
Where:
M = Mass of Earth
R = Radius of Earth
Example: On Moon, g ≈ 1.6 m/s²
🔹 Mass and Weight
Mass: Quantity of matter in a body (constant).
Weight: Force with which Earth attracts a body.
Formula:
Weight (W) = m × g
| Property | Mass | Weight |
|---|---|---|
| Definition | Amount of matter | Gravitational force |
| Unit | Kilogram (kg) | Newton (N) |
| Constant? | Yes | No (depends on g) |
| Quantity | Scalar | Vector |
Example:
Mass = 50 kg (everywhere)
Weight on Earth = 50 × 9.8 = 490 N
🔹 Gravitational Potential Energy
Energy possessed due to height in a gravitational field.
Formula:
PE = m × g × h
Example:
Mass = 2 kg, h = 10 m,
PE = 2 × 9.8 × 10 = 196 J
🔹 Equations of Motion under Gravity
When an object falls freely or is thrown upward:
Use these equations (replace a with g):
v = u + g × t
s = ut + (1/2) × g × t²
v² = u² + 2 × g × s
Example:
Ball thrown upward with u = 20 m/s,
Time to reach max height = v = 0,
t = (0 – 20) / -9.8 = 2.04 s
🔹 Thrust and Pressure
Thrust: Force applied perpendicular to a surface.
Pressure: Thrust per unit area.
Formula:
Pressure = Thrust / Area
| Quantity | Unit | Nature |
|---|---|---|
| Thrust | Newton (N) | Vector |
| Pressure | Pascal (Pa) | Scalar |
Example:
A woman in heels exerts more pressure than a man in flat shoes due to smaller area.
🔹 Pressure in Fluids
Liquids and gases exert pressure in all directions.
Formula:
Pressure = h × ρ × g
Where:
h = depth
ρ (rho) = density
g = acceleration due to gravity
Example: Deep-sea divers experience higher pressure due to large h.
🔹 Buoyancy and Archimedes’ Principle
Buoyancy: Upward force exerted by fluid.
Archimedes’ Principle: Body immersed in fluid experiences an upward force equal to the weight of fluid displaced.
Formula for Buoyant Force:
FB = ρ × g × V
Where:
V = Volume of fluid displaced
Example: A plastic ball floats while an iron ball sinks due to difference in density.
🔹 Relative Density
Ratio of density of a substance to density of water.
Formula:
Relative density = Density of substance / Density of water
No units (as it is a ratio).
Example: Relative density of gold = 19.3