Quick Revision Notes & Formula Sheet

Class 9 Science - Chapter: Gravitation (गुरुत्वाकर्षण)

MP Board - English Medium

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### 1. Introduction to Gravitation (परिचय)

• Gravitation: The force of attraction between any two objects in the universe.
• Gravity: A special case of gravitation where the force of attraction is exerted by the Earth on any object towards its center.

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### 2. Universal Law of Gravitation (सार्वभौमिक गुरुत्वाकर्षण का नियम)

Stated by Sir Isaac Newton. Every object in the universe attracts every other object with a force that is:

1. Directly proportional to the product of their masses (m1 and m2).
2. Inversely proportional to the square of the distance (d) between their centers.

Key Formula:

F = (G * m1 * m2) / d^2

Where:

• F = Gravitational force between two objects (Newton, N)
• m1 and m2 = Masses of the two objects (kg)
• d = Distance between the centers of the two objects (m)
• G = Universal Gravitational Constant

Universal Gravitational Constant (G):

• Value of G: 6.673 × 10^-11 N m^2 / kg^2
• Note: G is constant everywhere in the universe and does not depend on the medium or the distance between objects.

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### 3. Free Fall and Acceleration Due to Gravity (मुक्त पतन और गुरुत्वीय त्वरण)

• Free Fall: When an object falls towards the earth under the sole influence of gravity (ignoring air resistance), it is said to be in free fall.
• Acceleration due to Gravity (g): The uniform acceleration produced in a freely falling body due to the gravitational pull of the earth.

Key Formula:

g = (G * M) / R^2

Where:

• G = Universal gravitational constant
• M = Mass of the Earth (kg)
• R = Radius of the Earth (m)

Value of g on Earth:

• Standard average value: g = 9.8 m/s^2

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### 4. Difference Between g and G

Property	Acceleration due to Gravity (g)	Universal Gravitational Constant (G)
Definition	Acceleration experienced by a body in free fall.	Gravitational force between two unit masses kept at unit distance.
Type	It is a vector quantity.	It is a scalar quantity.
Value	It varies from place to place on Earth (max at poles, min at equator).	It is constant throughout the universe.
SI Unit	m/s^2	N m^2 / kg^2

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### 5. Mass and Weight (द्रव्यमान और भार)

• Mass (m):
  • The quantity of matter contained in a body.
  • SI Unit: Kilogram (kg)
  • It is a scalar quantity and remains constant everywhere.
• Weight (W):
  • The force with which the Earth attracts an object.
  • Formula: W = m × g
  • SI Unit: Newton (N)
  • It is a vector quantity and changes depending on the value of g at that place.

Important Fact: Weight of an object on the Moon is about 1/6th of its weight on the Earth because the gravitational pull of the moon is 1/6th of the Earth's. Weight on Moon = (1 / 6) × Weight on Earth

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### 6. Thrust and Pressure (प्रणود और दाब)

• Thrust: The total force acting perpendicular (at right angles) to a surface.
  • SI Unit: Newton (N)
• Pressure (P): The force acting per unit area of a surface.

Key Formula:

Pressure (P) = Thrust / Area = F / A

• SI Unit of Pressure: Newton per square meter (N/m^2) or Pascal (Pa).
• Key Concept: Smaller the area, larger is the pressure for the same force (e.g., sharp needle, wide straps of school bags).

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### 7. Buoyancy and Archimedes' Principle (उत्प्लावकता और आर्किमिडीज़ का सिद्धांत)

• Buoyancy (Upthrust): The upward force exerted by a fluid (liquid or gas) on an object immersed in it.
• Buoyant Force: Objects sink or float based on the balance between gravitational pull (downward) and buoyant force (upward).
  • If Buoyant Force > Weight of object $\rightarrow$ Object Floats
  • If Buoyant Force < Weight of object $\rightarrow$ Object Sinks

Archimedes' Principle:

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

• Applications:
  1. Designing ships and submarines.
  2. Lactometers (used to determine the purity of milk).
  3. Hydrometers (used for finding density of liquids).

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### 8. Density and Relative Density (घनत्व और आपेक्षिक घनत्व)

• Density (d or ρ): Mass per unit volume of a substance.

  • Formula: Density = Mass / Volume (d = m / V)
  • SI Unit: kg/m^3

• Relative Density: The ratio of the density of a substance to the density of water.

  • Formula: Relative Density = Density of substance / Density of water
  • Note: Since it is a ratio of similar quantities, it has no SI unit.

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### 9. Equations of Motion for Freely Falling Bodies

When an object moves vertically under gravity, replace acceleration a with g and distance s with height h:

1. v = u + gt
2. h = ut + (1/2)gt^2
3. v^2 = u^2 + 2gh

(Sign Convention: Take g as positive when moving downwards, and negative (-g) when moving upwards against gravity).