Introduction to Gravitation and Acceleration Due to Gravity
Have you ever thought about why we always fall down on the earth? Why not upward? Do not worry, today what you need to do is learn from Newton's experience that made him think about the gravitational pull when an apple fell on his head.
Learn about Gravitation on Vedantu
Issac Newton discovered gravitation in the year 1665. Gravitation is the force of attraction between the two bodies in the universe.
Gravitation is a fascinating topic, and to make it more interesting, Vedantu offers a pro class for physics to learn from talented physics experts; experts use 3-D illustrated examples to explain gravity and its associated things.
In this chapter, you will learn one more term, i.e., acceleration due to gravity, that has an essential role in physics. It is the acceleration a body attains when it falls freely under gravity, 'g' represents the acceleration due to gravity.
Difference between Universal Gravitation Constant (G) and Acceleration Due to Gravity (g)
When two bodies feel the force of attraction under the universe, they feel the force equal to or greater than the universal gravitational constant. In simple words, it is the force of attraction two-unit mass bodies feel when they are near a unit distance from their centers.
Students often get confused between the symbols ‘G’ and ‘g’, but Vedantu has come up with the solutions to clear all the confusion. Vedantu not just helps you with the definitions and answers to the problems, it also readily distinguishes the topics. The subject matter expert of physics has explained the difference between the two terms in detail. Learning the difference between topics is essential to excel in them.
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Relation between G and g
In this topic, students also learn about the relation between the universal gravitational constant and acceleration due to gravity. Physics experts have given a detailed explanation in the notes, including the values and units of each quantity. The relation signifies that acceleration due to gravity (g) is directly proportional to the mass of the body to the square of the distance between two objects.
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In the notes, you will find Vedantu has mentioned the significance of gravity and the gravitational pull on the physics of the object. So that students can understand and observe the phenomenon effectively.
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FAQs on Relation Between G and g
1. What is the fundamental difference between the Universal Gravitational Constant (G) and acceleration due to gravity (g)?
The key difference between G and g lies in their nature and scope. 'G' is a universal constant, while 'g' is a variable.
- Universal Gravitational Constant (G): This is a scalar quantity, meaning it only has magnitude. Its value, 6.674 × 10⁻¹¹ N m²/kg², is the same everywhere in the universe. It represents the intrinsic strength of the gravitational force.
- Acceleration Due to Gravity (g): This is a vector quantity, possessing both magnitude and direction (towards the centre of the celestial body). Its value changes based on the mass and radius of the planet or moon. On Earth's surface, its average value is approximately 9.8 m/s².
2. How do you derive the formula for the relation between g and G?
The relation between g and G can be derived by equating Newton's Universal Law of Gravitation with Newton's Second Law of Motion. Consider an object of mass 'm' on the surface of the Earth, which has mass 'M' and radius 'R'.
- According to the Universal Law of Gravitation, the force (F) on the object is: F = G * (M*m) / R².
- According to the Second Law of Motion, the force on the object due to gravity is its weight: F = m * g.
- By equating both expressions for force, we get: m * g = G * (M*m) / R².
- Cancelling the mass of the object 'm' from both sides gives the final relation: g = GM / R².
3. Why is the Universal Gravitational Constant (G) considered a scalar quantity?
The Universal Gravitational Constant (G) is considered a scalar quantity because it only has a magnitude and no associated direction. It is a fundamental constant of nature that quantifies the strength of the gravitational attraction between two masses. The force itself is a vector, but 'G' is simply the constant of proportionality in the equation and does not point in any specific direction.
4. Why is acceleration due to gravity (g) considered a vector quantity?
Acceleration due to gravity (g) is a vector quantity because it possesses both magnitude and direction. Its magnitude is the rate at which an object's velocity changes when falling (e.g., 9.8 m/s² on Earth), and its direction is always towards the center of the massive body (like Earth) that is exerting the gravitational pull.
5. How does the value of 'g' change with altitude above the Earth's surface?
The value of acceleration due to gravity (g) decreases as you move to a higher altitude from the Earth's surface. If 'g' is the value at the surface (radius R) and 'g'' is the value at a height 'h' above the surface, the relation is given by: g' = g * [R / (R+h)]². This shows that as the altitude 'h' increases, the value of g' decreases because the distance from the Earth's center increases.
6. Why is 'G' called the "Universal" Gravitational Constant?
'G' is called the "Universal" Gravitational Constant because its value is believed to be the same throughout the entire universe, regardless of location, time, or the chemical composition of the masses involved. Unlike 'g', which is specific to a planet or moon, 'G' is a fundamental constant that governs gravitational interactions everywhere, from apples falling on Earth to galaxies colliding in deep space.
7. How does the value of 'g' vary as we go deeper into the Earth?
Interestingly, the value of 'g' also decreases as we go deeper into the Earth. This is because as you descend, the mass of the Earth pulling you towards the center decreases. Only the mass of the sphere below you contributes to the net gravitational force. At the exact center of the Earth, the value of 'g' would be zero, as the mass pulling you is equal in all directions.
8. Does the value of acceleration due to gravity (g) depend on the mass of the falling object?
No, the value of acceleration due to gravity (g) does not depend on the mass of the falling object. As seen in the derivation g = GM/R², the formula only includes the mass of the Earth (M) and its radius (R), not the mass of the smaller object ('m'). This is why, in a vacuum where there is no air resistance, a feather and a bowling ball dropped from the same height will hit the ground simultaneously.
9. If 'g' is the same for all objects, why does a feather fall slower than a hammer in the air?
This is a common point of confusion that is explained by the presence of air resistance, which is a form of friction. While gravity pulls both the feather and the hammer with the same acceleration (g), the opposing force of air resistance has a much greater effect on the feather due to its large surface area and low mass. The hammer, being dense and compact, is less affected by air resistance and falls faster. In a vacuum, they would fall at the same rate.
10. What would happen to planets and satellites if the gravitational force suddenly disappeared?
If the gravitational force were to suddenly disappear, celestial bodies would no longer be held in their orbits. According to Newton's First Law of Motion (the law of inertia), an object in motion stays in motion with the same speed and in the same direction unless acted upon by an external force. Without gravity, a planet would stop orbiting the Sun and fly off into space in a straight line tangent to its original orbital path. The same would happen to satellites orbiting planets.
