Relation Between G and g Overview
G and g are two commonly used quantities when discussing gravitational force. The acceleration owing to gravity is denoted by small g, whereas the universal gravitational constant is denoted by large G.
What is Gravitational Force?
With a force known as Gravitational Force, each body in our universe draws other bodies towards itself. As a result, gravitation is the study of the interaction of two masses. The heavier of the two masses is referred to as the source mass, while the lighter is referred to as the test mass. Gravitational force is a central force that acts along the line connecting the centers of the two masses and is only dependent on the location of the test mass relative to the source mass.
Gravitational Force Formula
The following is the formula for gravitational force-
F = Gm₁m₂/r²
Where,
F denotes the gravitational force between two objects in Newton (N).
m₁is the mass of one massive body in kilograms.
m₂is the mass in kilograms of another enormous entity.
The distance between them is measured in kilometers (km).
The universal gravitational constant G has the value 6.674 x 10⁻¹¹ Nm²/Kg².
Relation Between G and g Definitions
Acceleration due to Gravity (g)
Any object's acceleration owing to gravity is represented by a small g. This is usually reserved for big objects because little things have relatively little gravitational force. Small g is the rate of change in velocity caused by gravitational pull. This is a form of acceleration caused only by gravitational force. Because this is an acceleration, the unit is meters per second squared (m/s²). So, when we drop an object, the acceleration it experiences is due to the gravitational force of the Earth, and we may refer to this acceleration as the Earth's gravity acceleration. The value of g for planet Earth is 9.8 m/s². It varies for different items depending on their mass and size.
Universal Gravitational Constant (G)
The universal gravitational constant is denoted by the letter G. It is a constant value with a value of 6.67408 x 10⁻¹¹ m³ kg⁻¹ s⁻². Its value is constant and does not change from object to object, with a unit of m³ kg⁻¹ s⁻².
Relation Between G and g Formula
In physics, G, and g are connected as follows-
g = GM/R²
Where,
g -The acceleration due to gravity is measured in m/s².
G - denotes the universal gravitational constant, which is measured in Nm²/kg².
R - is the enormous body's radius in kilometers.
M - is the huge body's mass in kilograms.
Although there is a formula in physics to represent the relationship between g and G, there is no relationship between acceleration due to gravity and the universal gravitational constant since the value of G is constant. The value of G is constant at any location in the universe, and G and g are not related.
Relation Between G and g
In physics, G and g are different things. The table below shows the difference between G and g.
|
Particulars |
Symbols |
Definition |
Value of Planet Earth |
Nature of Value |
Units |
|
Acceleration due to gravity |
g |
The acceleration felt by a body in free fall as a result of the large body's gravitational pull. |
9.8 m/s² |
Variable from location to location. |
m/s² |
|
Universal Gravitational Constant |
G |
The force of attraction between two objects of equal mass is separated by an equal distance everywhere in the universe. |
6.67 x 10⁻¹¹ Nm²/Kg² |
At whatever place in our cosmos, it is constant. |
Nm²/kg² |
Derivations of Relation Between G and g
The universal law of gravity states that-
F = GMm/R² ….. (1)
We know from Newton's second rule of motion that-
F = ma ….. (2)
If the gravitational acceleration at a particular place is g, then the previous equation becomes-
F = mg ….. (3)
Substituting equation (3) into (1) yields-
m/g = GMm/R²
When we simplify the preceding equation, we get-
g = Gm/R²
As a result, the connection between g and G is -
g = Gm/R²
Read more about the Uniform Motion Definition.
What is the Relation Between G and g on Earth?
We arrived at the following relation between G and g-
g = Gmm₁/r²
We can calculate the acceleration due to gravity on Earth by plugging in the values of m₁and r for the Earth. Because our globe is an ellipsoid, the radius at the equator is bigger than the radius at the poles. Because gravity's acceleration is inversely proportional to distance squared, the value of g near the equator is larger than that of g at the poles. The value of g fluctuates very little, from roughly 9.78 9.8 m/s² near the equator to around 9.83 9.8 m/s² at the poles. The value of G, on the other hand, is thought to stay constant throughout the cosmos.
Difference Between G and g
The following table depicts the differences between G and g-
|
Gravitation (G) |
Gravity (g) |
|
Gravitation is the attractive force that exists between any two bodies in the cosmos. |
Gravity is the gravitational force of the earth on a body that is close to the earth's surface. |
|
The Universal Gravitational Constant is denoted by the letter G. |
The acceleration owing to gravity is denoted by g. |
|
It is a feeble power. |
It is a powerful force. |
|
Scalar Quantity |
Vector Quantity |
|
It takes two masses. |
It only takes one mass. |
|
The value of G remains constant throughout. (G = 6.67 x 10⁻¹¹ Nm²/Kg²) |
The value of g fluctuates depending on where you are on the planet. |
|
F = GM₁M₂/r² (G = gravitational constant) is the force. |
F = m x g (g = acceleration due to gravity) is the force. |
Read more about Oscillatory Motion.
Conclusion
Gravity is proportional to mass production and inversely proportional to the square of the distance between masses. Gravity is defined as the product of a body's mass and its gravitational acceleration over time. The gravitational force exerted by the earth is known as gravity. The weight of a body can change, but its mass remains constant. Gravity's acceleration is tiny g, yet the universal gravitational constant is large G. When a body is at rest on the earth's surface, it is impacted by the gravitational pull of the earth.
Sample Questions for Relation Between G and g
Sample Question 1: What is the mass of a body on the moon if it has a mass of 9.8 kg on Earth?
Solution: On the moon, it will remain the same, weighing 9.8 kg.
Sample Question 2: What happens to the gravitational force between two bodies if one of their masses is doubled?
Solution: When the mass of a body is doubled, so does its force.
Sample Question 3: What does a low G value imply?
Solution: A low G value indicates that the gravitational pull between two ordinary-sized objects is weak.
Sample Question 4: An apple is attracted to the dirt. Is the apple a magnet for the Earth as well? If that's the case, why isn't the earth gravitating towards the apple?
Solution: According to Newton's third rule of motion, action, and reaction are equal and opposing. It denotes that the force exerted by the earth's pull on the apple is equal to the force exerted by the apple on the earth. We do, however, know that acceleration is 1/m. Because the earth's mass is so vast in relation to the apple's, the earth's acceleration will be so modest that it will go undetected.
Sample Question 5: What is the significance of the symbol 'G' for the universal gravitational constant?
Solution: The constant 'G' is universal since it is unaffected by the type and size of bodies, the space in which they are held, or the time when the force is evaluated.