An object that falls under the sole influence of gravity is known as a free-falling object. A free-falling object has an acceleration of 9.8 m/s^{2}, downward (on Earth). This numerical value is so significant that it is given a special name as the acceleration of gravity. We denote it with the symbol g.
The force of attraction between any two unit masses separated by a unit distance is called the universal gravitational constant. The universal gravitational constant is denoted by the symbol G and is measured in Nm^{2}/kg^{2}. The numerical value of G is 6.67 × 10^{-11} Nm²/Kg².
The relation between G and g is not proportional. This means that they are independent entities.
Relationship Between G and g
In physics, G and g related to each other as follows:
\(g=\frac{GM}{R^{2}}\) |
Where,
- g is the acceleration due to the gravity measured in m/s^{2}.
- G is the universal gravitational constant measured in Nm^{2}/kg^{2}.
- R is the radius of the massive body measured in km.
- M is the mass of the massive body measured in Kg
Although there exists a formula to express the relation between g and G in physics, there is no correlation between acceleration due to gravity and universal gravitation constant, as the value of G is constant. The value of G is constant at any point in this universe, and G and g are not dependent on each other.
What is G and g?
The G and g are distinct entities in physics. Below is the table of the difference between G and g.
Symbol | Definition | Nature of Value | Unit | |
Acceleration due to gravity |
g | The acceleration experienced by a body under free fall due to the gravitational force of the massive body | Changes from place to place.
Acceleration due to gravity of the earth is 9.8 m/s^{2} |
m/s^{2} |
Universal Gravitational Constant |
G | The force of attraction between two objects with unit mass separated by a unit distance at any part of this universe. | Constant at any point in this universe.
G = 6.67×10^{-11 }Nm^{2}/kg^{2} |
Nm^{2}/kg^{2} |
Deriving the relationship between g and G
According to the universal law of gravitation,
\(F=\frac{GMm}{R^{2}}\) ————(1)From Newton’s second law of motion, we know that
\(F={m}{a}\) ———–(2)If the acceleration due to gravity is g at a given point, then the above equation becomes
\(F={m}{g}\) ———–(3)Substituting equation (3) in (1), we get-
\(mg=\frac{GMm}{R^{2}}\)Simplifying the above equation, we get
\(g=\frac{GM}{R^{2}}\)Thus, we arrive at the relationship between g and G as –
\(\Rightarrow g=\frac{GM}{R^{2}}\)Physics Related Topics:
Gravity Waves |
Relation Between Density And Temperature |
Relation Between Escape Velocity And Orbital Velocity |
Relation Between Critical Angle And Refractive Index |
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