Gravitation

Gravitation

Table of Contents

Introduction of Gravitation

Gravitational Force:

  • Natural force of attraction between massive objects.
  • It is one of the four fundamental forces in the universe, along with electromagnetism, strong nuclear force, and weak nuclear force.

Significance in the Universe:

  • Shapes the motion of celestial bodies like planets, stars, and galaxies.
  • Plays a crucial role in determining the structure and evolution of the universe.

Isaac Newton:

  • Renowned scientist who formulated the Law of Universal Gravitation.
  • His work revolutionized our understanding of gravity and its effects on objects.
  • Newton’s Principia Mathematica (1687) introduced the mathematical principles of gravitation.
  • Unified the earthly and celestial realms under a single law.

Newton’s Law of Gravitation

  • Mass: Quantity of matter in an object.
  • Distance: Separation between two objects.
  • Gravitational Constant (G): Universal constant, denoted by .

Mathematical Formulation

  • Formula:
  • Explanation of the Formula:
    • Dependence on Mass: Force is directly proportional to the product of the masses .
    • Dependence on Distance: Force is inversely proportional to the square of the distance .
    • Inverse Square Law: Force decreases with the square of the distance between two objects.

Applications of Newton’s Law

  • Motion of Planets: Governs the orbits of planets around the sun.
  • Satellites: Helps in understanding the motion and stability of artificial satellites.
  • Falling Objects: Describes the gravitational pull on objects on Earth.
  • Weight vs. Mass: Weight is the force due to gravity acting on an object, while mass is the amount of matter in an object.

Solved Examples

Question: What is the force of attraction between two objects of masses 10 kg and 20 kg placed 5 meters apart? (Given )

    • Answer:

Applications of Newton’s Law of Gravitation


Motion of Planets:

Solar System Planet Labels GIF | GIFDB.com

Gravitational Force:

  • Responsible for the orbit of planets around the sun.

Kepler’s Laws:

Laws Of Planetary Motion" Images – Browse 57 Stock Photos, Vectors, and  Video | Adobe Stock

Brief explanation:

  • First Law: Planets move in elliptical orbits with the sun at one focus.
  • Second Law: A line segment joining a planet and the sun sweeps out equal areas during equal intervals of time.
  • Third Law: The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

Satellites:

Mathematics of Satellite Motion

Orbit Maintenance:

  • Satellites are kept in orbit due to the gravitational force between the satellite and the Earth.

Applications in Communication:

  • Gravitational force ensures satellite communication by keeping satellites in their designated geostationary or polar orbits.

Importance in Remote Sensing:

  • Gravitational force aids in remote sensing operations, allowing satellites to gather data about Earth’s surface, atmosphere, and oceans.

Falling Objects:

Difference Between Weight and Mass:

  • Mass: Amount of matter in an object, measured in kilograms (kg).
  • Weight: Force exerted on an object due to gravity, measured in newtons (N).

Calculation of Weight:

  • Formula:
    • m: Mass of the object (in kg).
    • g: Acceleration due to gravity (approximately 9.8 m/s2 on Earth).

Gravitational Constant (G)

Gravitational Constant (G): A fundamental constant that appears in the formula for Newton’s Law of Gravitation.

Significance: It quantifies the strength of the gravitational force between two objects based on their masses and the distance between them.

Experimental Determination of G

Henry Cavendish’s Experiment (1797-1798): One of the earliest and most famous experiments to determine the value of G.

  • Cavendish used a torsion balance to measure the weak gravitational attraction between small masses.
  • The experiment provided an indirect way to determine G by measuring the torsional effect of gravitational attraction.

Value of G in SI Units

SI Unit: Newton meter squared per kilogram squared

Value of g on Earth is 9.8 m/s2

Conclusion


  • Recap of Newton’s Law of Gravitation:

    • Gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.
    • Mathematical formulation: F=G×r2m1×m2
  • Emphasizing the universal applicability of gravitational force:

    • Celestial phenomena: Responsible for the motion of planets, orbiting satellites, and the relationship between celestial bodies.
    • Terrestrial phenomena: Dictates the weight of objects on Earth’s surface, falling objects, and the tides due to the Moon’s gravitational pull.
  • Highlighting the importance of understanding gravitation for explaining and predicting a wide range of physical phenomena both in the cosmos and on Earth.

FAQ’s

Gravitation is the universal force of attraction between objects with mass. Simply put, it’s what makes things fall down and keeps planets in orbit.

Gravity is a pull between objects. The more massive an object, the stronger its pull.

In high school physics, you’ll learn about Newton’s Law of Universal Gravitation. This law states that every object with mass attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

There aren’t exactly three “laws” of gravitation. However, there’s one fundamental law – Newton’s Law of Universal Gravitation – that explains the attractive force between objects.

The formula for Newton’s Law of Universal Gravitation is:

F = G * (M1 * M2) / r^2

  • F is the gravitational force (measured in Newtons)
  • G is the gravitational constant (a fixed value, approximately 6.6743 × 10^-11 m^3 kg^-1 s^-2)
  • M1 and M2 are the masses of the two objects (measured in kilograms)
  • r is the distance between the centers of the objects (measured in meters)

Newton’s Third Law of Motion (not directly related to gravity) states that for every action, there is an equal and opposite reaction. This applies to gravity as well. When two objects attract each other gravitationally, the force of attraction is mutual. They both pull on each other with the same amount of force.

MCQ’s

1. What is the force that attracts objects towards each other due to their mass?
a) Magnetism
b) Friction
c) Gravitation
d) Elasticity
Answer: c) Gravitation


2. Who formulated the law of universal gravitation?
a) Isaac Newton
b) Albert Einstein
c) Galileo Galilei
d) Johannes Kepler
Answer: a) Isaac Newton


3. What does the gravitational force between two objects depend on?
a) Mass of one object
b) Distance between the objects
c) Both mass and distance
d) Neither mass nor distance
Answer: c) Both mass and distance


4. Which planet has the strongest gravitational pull?
a) Mars
b) Earth
c) Jupiter
d) Saturn
Answer: c) Jupiter


5. What is the acceleration due to gravity on the surface of the Earth?
a) 5 m/s²
b) 9.8 m/s²
c) 12 m/s²
d) 15 m/s²
Answer: b) 9.8 m/s²


6. What is the SI unit of gravitational force?
a) Newton
b) Joule
c) Watt
d) Volt
Answer: a) Newton


7. Which of the following statements is true regarding gravitational force?
a) It is a repulsive force
b) It acts in the opposite direction of the mass
c) It is a contact force
d) It acts between any two objects in the universe
Answer: d) It acts between any two objects in the universe


8. If the distance between two masses is doubled, how will the gravitational force between them change?
a) Halves
b) Doubles
c) Quadruples
d) Remains the same
Answer: a) Halves


9. What happens to the weight of an object when taken to the Moon’s surface compared to its weight on Earth?
a) Increases
b) Decreases
c) Remains the same
d) Becomes zero
Answer: b) Decreases


10. Which law states that every point mass attracts every other point mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them?
a) Kepler’s first law
b) Kepler’s second law
c) Newton’s first law
d) Newton’s law of universal gravitation
Answer: d) Newton’s law of universal gravitation


11. Which law describes the gravitational force between two masses?

A) Kepler’s Law

B) Ohm’s Law

C) Newton’s Law of Gravitation

D) Hooke’s Law

Answer: C) Newton’s Law of Gravitation

12. The gravitational constant has the unit of:

A) N

B) m/s

C) Nm/kg^2

D) m^2/kg

Answer: C) Nm/kg^2

13. The force of attraction between two masses decreases as:

A) Mass increases

B) Distance decreases

C) Mass decreases

D) Distance increases

Answer: D) Distance increases

14. Weight is the measure of:

A) Volume

B) Mass

C) Gravitational force on an object

D) Density

Answer: C) Gravitational force on an object

15. The gravitational force between two masses will be maximum when the distance is:

A) Minimum

B) Maximum

C) Average

D) Constant

Answer: A) Minimum

16. If the distance between two masses is tripled, the gravitational force becomes:

A) 1/3 times

B) 1/9 times

C) 3 times

D) 9 times

Answer: B) 1/9 times

17. Which factor does NOT affect the gravitational force between two masses?

A) Mass of the first object

B) Mass of the second object

C) Distance between the objects

D) Volume of the objects

Answer: D) Volume of the objects

18. The gravitational force is weakest on:

A) Moon

B) Earth

C) Sun

D) Mars

Answer: A) Moon

19. Which law states that every mass attracts every other mass in the universe 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?

A) Newton’s First Law

B) Newton’s Second Law

C) Newton’s Third Law

D) Newton’s Law of Gravitation

Answer: D) Newton’s Law of Gravitation

 

  • Units and dimensions
  • Measurement and Error Analysis
  • Kinematics
  • Dynamics
  • Motion
  • Circular Motion
  • Energy and Momentum
  • Gravity
  • Fluid Mechanics
  • Oscillations and Waves
  • Thermodynamics
  • Laws of Thermodynamics
  • Heat Transfer
  • Electric Field, Forces and Potential
  • Work, energy, and power
  • Gravitation
  • Floatation
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