CBSE Class 9 Science Notes: Gravitation

Universal Law of Gravitation

Definition: The universal law of gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Core Principles:

Every object with mass exerts a gravitational force.
The force is always attractive.
The strength of the force depends on the masses of the objects and the distance between them.

Formula: The gravitational force (F) between two objects is given by: $F = G \frac{m_1 m_2}{r^2}$ where:

$G$ is the universal gravitational constant ($6.674 \times 10^{-11} N m^2 kg^{-2}$),
$m_1$ and $m_2$ are the masses of the two objects,
$r$ is the distance between the centers of the two objects.

Examples: The force that keeps the planets in orbit around the Sun, the force causing objects to fall towards the Earth.

Gravity and Gravitational Force on Earth

Definition: Gravity is the force of attraction exerted by the Earth on objects near its surface. This is a special case of gravitational force where one object is the Earth.

Core Principles:

Earth’s large mass causes a significant gravitational pull.
This force pulls objects towards the center of the Earth.
The gravitational force is responsible for keeping us grounded.

Acceleration Due to Gravity

Definition: The acceleration experienced by an object due to the Earth’s gravitational force. It is denoted by ‘g’.

Core Principles:

All objects near the Earth’s surface accelerate downwards at the same rate (approximately).
This acceleration is independent of the object’s mass (in a vacuum).

Formula: $g = G \frac{M}{R^2}$ where:

$G$ is the universal gravitational constant,
$M$ is the mass of the Earth,
$R$ is the radius of the Earth.

The value of $g$ on Earth is approximately $9.8 \, m/s^2$.

Difference Between Mass and Weight

Definitions:

Mass: The measure of the amount of matter in an object. It is a scalar quantity.
Weight: The force of gravity acting on an object. It is a vector quantity.

Core Differences:

Mass is constant; weight varies depending on the gravitational force.
Mass is measured in kilograms (kg); weight is measured in Newtons (N).
Weight = Mass x Acceleration due to gravity ($W = mg$).

Concept of Free Fall

Definition: The motion of an object solely under the influence of gravity, with no other forces acting upon it (neglecting air resistance).

Core Principles:

The only force acting on the object is gravity.
The object accelerates downwards at a rate of $g$.
The object’s initial velocity affects its motion.

Examples: A ball dropped from a height, a falling stone (neglecting air resistance).

Thrust and Pressure

Definitions:

Thrust: The force acting perpendicular to a surface.
Pressure: The thrust acting per unit area.

Formula: $Pressure = \frac{Thrust}{Area}$

Units:

Thrust is measured in Newtons (N).
Area is measured in square meters ($m^2$).
Pressure is measured in Pascals (Pa), where 1 Pa = 1 N/$m^2$.

Examples: The pressure exerted by a nail on a surface, the pressure exerted by a fluid.

Buoyant Force

Definition: The upward force exerted by a fluid on an object immersed in it.

Core Principles:

Also known as upthrust.
Acts in the opposite direction to the force of gravity.
The buoyant force is due to the pressure difference between the top and bottom of the object.

Archimedes’ Principle

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

Implications:

Explains why some objects float and some sink.
Important in the design of ships and submarines.

Conditions for Floating and Sinking

Core Principles:

Floating: An object floats if the buoyant force acting on it is equal to or greater than its weight. This occurs when the object’s density is less than or equal to the density of the fluid.
Sinking: An object sinks if its weight is greater than the buoyant force acting on it. This occurs when the object’s density is greater than the density of the fluid.

Density and Buoyancy: