Grade 9
  1. Mechanics  1.1. Motion  1.1.1. Types of motion  1.1.2. Distance and displacement  1.1.3. Speed and Velocity  1.1.4. Acceleration  1.1.5. Graphical representation of motion  1.1.6. Equations of motion  1.1.7. Uniform and non-uniform motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Relative speed  1.1.10. Circular motion  1.2. Laws of force and motion  1.2.1. The concept of force  1.2.2. newton's first law of motion  1.2.3. Newton's second law of motion  1.2.4. Newton's third law of motion  1.2.5. Inertia and types of inertia  1.2.6. Motion  1.2.7. Conservation of momentum  1.2.8. Application of Newton's laws in daily life  1.2.9. Types of Forces (Contact and Non-Contact)  1.2.10. Friction and its effects  1.3. Gravitational force  1.3.1. Newton's law of universal gravitation  1.3.2. Importance of Gravitational Force  1.3.3. Acceleration due to gravity  1.3.4. Free fall and weightlessness  1.3.5. Mass and weight  1.3.6. Variation of g with height and depth  1.3.7. Kepler's laws of planetary motion  1.3.8. Satellites and their orbits  1.4. Work, Energy and Power  1.4.1. Concept of work  1.4.2. Positive and negative actions  1.4.3. Work done by constant and variable force  1.4.4. Energy and its forms  1.4.5. Kinetic energy and potential energy  1.4.6. Law of conservation of energy  1.4.8. Commercial unit of energy  1.4.9. Work–energy theorem  1.5. Simple machines  1.5.1. Types of simple machines  1.5.2. Mechanical advantage  1.5.3. Machine efficiency  1.5.4. Levers and their types  1.5.5. Pulleys and Inclined Planes  1.5.6. Gears and their uses
  2. Properties of matter  2.1. States of matter  2.1.1. Solids, liquids and gases  2.1.2. Properties of different states of matter  2.1.3. Change in state of matter  2.1.4. Plasma and Bose–Einstein condensate  2.2. Density and pressure  2.2.1. Concept of density and relative density  2.2.2. Pressure in solids, liquids and gases  2.2.3. Pascal's law and its applications  2.2.4. Atmospheric pressure and its variations  2.2.5. Surface tension and capillarity  2.3. Buoyancy and Archimedes' principle  2.3.1. Buoyant force  2.3.2. Archimedes principle  2.3.3. Applications of Archimedes' Principle  2.3.4. floating and sinking objects  2.3.5. Theory of Flotation and Archimedes' Principle
  3. Heat and Thermodynamics  3.1. Temperature and heat  3.1.1. Concept of heat and temperature  3.1.2. Temperature measurement  3.1.3. Temperature scales  3.2. Heat transfer  3.2.1. Conduction of heat  3.2.2. Convection of heat  3.2.3. heat radiation  3.2.4. Applications of heat transfer  3.2.5. Thermal conductivity  3.3. Thermal expansion  3.3.1. Expansion of solids, liquids and gases  3.3.2. Abnormal expansion of water  3.3.3. Applications of Thermal Expansion  3.4. Specific heat capacity and latent heat  3.4.1. Concept of specific heat capacity  3.4.2. Measurement and applications of specific heat  3.4.3. Latent heat of fusion and vaporization  3.4.4. Heat Engines and Efficiency
  4. Waves and sound  4.1. Waves and their types  4.1.1. Mechanical and electromagnetic waves  4.1.2. Longitudinal and Transverse Waves  4.1.3. Properties of Waves  4.1.4. Wavelength, frequency and speed of the wave  4.1.5. Superimposition of waves  4.2. Sound waves  4.2.1. Nature and transmission of sound  4.2.2. Speed of sound in different mediums  4.2.3. Reflection of sound and echo  4.2.4. Sonar and ultrasound  4.2.5. Resonance and pulsation  4.3. Sound characteristics  4.3.1. Intensity, loudness and quality of sound  4.3.2. Doppler effect in sound
  5. Lighting and Optics  5.1. Reflection of light  5.1.1. Laws of reflection  5.1.2. Reflection from a plane mirror  5.1.3. Reflection from a spherical mirror  5.1.4. Image formation by concave and convex mirrors  5.1.5. Applications of Reflection  5.2. Refraction of light  5.2.1. Laws of refraction  5.2.2. Refractive index  5.2.3. Refraction through a glass slab  5.2.4. Refraction in water and air  5.2.5. Lenses and their types  5.2.6. Image formation by convex and concave lenses  5.2.7. Total internal reflection and its applications  5.3. Dispersion and scattering of light  5.3.1. Spectrum of white light  5.3.2. Prisms and Dispersion  5.3.3. Tyndall effect and blue sky
  6. Electricity and Magnetism  6.1. Electric charge and static electricity  6.1.1. The concept of electric charge  6.1.2. Charging by friction, contact and induction  6.1.3. Electroscope and its working  6.2. Current Electricity  6.2.1. The concept of electric current  6.2.2. Ohm's Law and Resistance  6.2.3. Factors affecting resistance  6.2.4. Series and Parallel Circuits  6.2.5. Heating effect of electric current  6.2.6. Electric power and energy  6.3. Magnetism  6.3.1. Natural and artificial magnets  6.3.2. Properties of magnets  6.3.3. Earth's magnetism  6.3.4. Magnetic field and field lines  6.3.5. Electromagnets and their applications
  7. Modern Physics  7.1. structure of the atom  7.1.1. Atomic Structure and Subatomic Particles  7.1.2. Electrons, Protons, and Neutrons  7.1.3. Rutherford and Bohr model  7.2. Radioactivity  7.2.1. Types of radioactive emissions  7.2.2. Half-life and radioactive decay  7.2.3. Uses and Hazards of Radioactivity
  8. Space science and astronomy  8.1. The universe and its components  8.1.1. Stars and galaxies  8.1.2. Planets and Solar System  8.2. Satellites  8.2.1. Natural and artificial satellites  8.2.2. Use of satellites

Grade 9 → Mechanics → Gravitational force ↓


Newton's law of universal gravitation


Newton's law of universal gravitation is a fundamental concept of physics that describes the gravitational attraction between objects with mass. According to this law, 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 their centers.

In simple terms, this means that any two objects, no matter how far apart they are, exert a pull on each other. This force is called the force of gravity.

Formula

The formula to calculate the gravitational force between two objects is as follows:

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

Where:

  • F is the gravitational force between the objects in newtons (N).
  • G is the gravitational constant. Its approximate value is 6.674 × 10⁻¹¹ N(m/kg)².
  • The masses of both objects m1 and m2 are in kilograms.
  • r is the distance between the centers of the two objects in meters (m).

Understanding the concept with examples

Let us understand the concept of gravitational force in depth with some examples and explanations:

Example 1: Gravitational force between the Earth and an object

Consider an object with mass m on the surface of the Earth. The Earth exerts a gravitational force on this object. The mass of the Earth is 5.972 × 10²⁴ kg, and the mean radius of the Earth is 6.371 × 10⁶ m.

F = G * (m_earth * m_object) / r_earth²

If the mass of the object is, say, 10 kg, then by substituting the values, we can calculate the gravitational force exerted on the object.

Example 2: Gravitational force between two people

Imagine two people standing 1 m apart, each with a mass of 70 kg. According to the universal law of gravitation, they also exert a gravitational force on each other.

F = G * (70kg * 70kg) / (1m)² F = 6.674 × 10⁻¹¹ * 4900 F = 3.27026 × 10⁻⁷ N

This force is extremely small, which explains why we don't feel gravitational attraction from everyday objects.

Visual representation

M₁ M₂ R The gravitational force acts along the line joining the centres of two masses.

Inverse relationship

The formula shows that the gravitational force decreases with the square of the distance. So, if the distance between two objects is doubled, the gravitational force becomes one-fourth of its original value. This inverse square law is important in understanding phenomena such as why gravity is weaker at higher altitudes.

Gravitational constant

The gravitational constant, G, is an important part of the formula. It is a universal constant, meaning its value does not change and remains the same throughout the universe. This small value explains why gravity is a weak force compared to others such as electromagnetism.

Applications of universal gravitation

Universal gravitation is important to understanding many natural phenomena:

  • Astronomy: It explains the orbits of planets and natural satellites, and the motions of celestial bodies.
  • Tidal force: The gravitational force of the Moon on the Earth causes tides in the oceans.
  • Space exploration: Calculating trajectories for spacecraft involves understanding gravitational interactions with other celestial bodies.

Newton's law of universal gravitation remains the basis of our understanding of the universe, highlighting the interconnection of all matter through gravity. Despite being one of the fundamental forces, gravity plays a versatile and vital role in both the vast universe and the environment around us.

Textual problem solving

Problem 1: Calculating the force of gravitation

Suppose two spheres of masses 10 kg and 20 kg are at a distance of 2 m from each other. Calculate the gravitational force between them.

F = G * (m1 * m2) / r^2 F = 6.674 × 10⁻¹¹ * (10 * 20) / 2² F = 6.674 × 10⁻¹¹ * 200 / 4 F = 3.337 × 10⁻¹⁰ N

This force is extremely small, which explains why such gravitational attraction is not noticeable in everyday experiences.

Problem 2: Understanding the distance effect

If the distance in the previous problem is halved, what will be the new gravitational force?

New r = 1 m F = G * (m1 * m2) / (1²) F = 6.674 × 10⁻¹¹ * 200 / 1 F = 1.3348 × 10⁻⁹ N

The force increased when the distance was halved, which shows an inverse square relationship.

Conceptual question

To understand Newton's law of universal gravitation better, consider the following questions:

  1. If the mass of both the objects is doubled and the distance is kept constant then what will be the change in the force?
  2. Consider what effect it would have on the gravitational force if both the mass and distance of an object were doubled.

Conclusion

Newton's law of universal gravitation provides important insight into how all objects with mass are connected to one another through gravity. By examining how mass and distance affect the force of gravity, we gain insight into the natural forces that shape our world and universe.

While gravity is an inherent and invisible force in our daily lives, its effects are much more profound - from the simple act of an object falling to the majestic dance of planets and stars in the cosmic arena. As we have discovered, Newton's insights help solve the mysteries of gravitational interactions, which underlie many aspects of physics and astronomy.


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Newton's law of universal gravitation

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