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 ↓


Variation of g with height and depth


The concept of gravity is something we encounter in our everyday lives. When an apple falls from a tree, or when we jump and come back down, it is all due to gravity. The gravitational force on an object near the Earth's surface is straight and is usually constant. However, this gravitational force can change slightly depending on where you are in relation to the Earth's surface. This is explained by the "variation of g with height and depth".

Understanding gravity (g)

The symbol "g" represents the acceleration due to gravity. At the surface of the Earth, it is about 9.8 m/s². This value tells how fast an object will accelerate when it is in free fall.

Imagine you are tossing a ball straight up in the air. The ball goes up, pauses for a moment, and then comes back down. The reason the ball comes back down is that it is constantly being pulled by Earth's gravity at a rate of about 9.8 m/s².

Variation of g with altitude

When you move away from the surface of the Earth, for example, if you climb a mountain or fly in an airplane, the distance between you and the center of the Earth increases. This increase in distance causes a slight decrease in the value of "g".

The formula to understand how gravity changes with altitude is:

g' = g(1 - 2h/r)

In this formula:

  • g' is the gravity at the height.
  • g is normal gravity at the Earth's surface, 9.8 m/s².
  • h is the height above the Earth's surface.
  • R is the radius of the Earth, approximately 6,371,000 m.

Let's consider an example. Suppose you are standing at the top of Mount Everest, which is approximately 8,848 meters above sea level. Plug the values into the formula:

G' = 9.8 (1 - 2 * 8848 / 6,371,000)

Solving this will give you a slightly smaller value of g' than 9.8 m/s².

Here is a simple presentation:

Earth h = height

Variation of g with depth

The value of "g" also changes when we go inside the Earth's surface, for example into caves or mines. At greater depths, a portion of the Earth's mass is now above you, which affects how the force of gravity is calculated.

The formula that shows how gravity changes with depth is:

g' = g(1 - d/r)

In this formula:

  • g' is the gravity at the depth.
  • g is normal gravity at the Earth's surface, 9.8 m/s².
  • d is the depth below the Earth's surface.
  • R is again the radius of the Earth, about 6,371,000 m.

Suppose you are in a mine 3000 meters below the Earth's surface:

g' = 9.8 (1 - 3000 / 6,371,000)

When you calculate this you will see that g' will be slightly less than 9.8 m/s².

Conceptually it goes something like this:

Earth d = depth

Comparison of height and depth

We have seen that "g" decreases as we move both up and down from the surface of the Earth. However, the reasons for this are different:

  • At higher altitudes, the distance from the center of the Earth increases.
  • At greater depths, less of the Earth's mass will be beneath you.

In both cases, there is a slight reduction in gravity, which is negligible in everyday life but important for precise calculations needed in engineering, astrophysics and other fields.

Real-life implications

For engineers building tall buildings or flying high in the sky, it may be necessary to consider the variation of g to ensure accuracy in calculations. Similarly, for miners working deep below the Earth's surface, understanding this concept can improve safety and accuracy in their work.

While changes in g are quite small and usually not felt in everyday activities, they are of keen interest in research and fields that require high precision, such as space exploration. For example, satellites and space shuttles will consider how gravity decreases with altitude to calculate orbits and trajectories with high precision.

Conclusion

Understanding the variation of g with height and depth helps us understand the intricacies of gravitational physics. Although it is a subtle effect, it impacts many scientific, engineering, and technological fields.

Studying the change of g highlights the beauty and complexity of physics in explaining natural phenomena in our universe.


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Variation of g with height and depth

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