What Is The Relation Between G And G? - Definition, Nature Of Value, Unit

Relationship between G and g

In physics, G and g related to each other as follows:

\(\begin{array}{l}g=\frac{GM}{R^{2}}\end{array} \)

Where,

• g is the acceleration due to the gravity measured in m/s2.
• G is the universal gravitational constant measured in Nm2/kg2.
• 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/s2	m/s2
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 Nm2/kg2	Nm2/kg2

Deriving the relationship between g and G

According to the universal law of gravitation,

\(\begin{array}{l}F=\frac{GMm}{R^{2}} ————(1)\end{array} \)

From Newton’s second law of motion, we know that

\(\begin{array}{l}F={m}{a} ———–(2)\end{array} \)

If the acceleration due to gravity is g at a given point, then the above equation becomes

\(\begin{array}{l}F={m}{g} ———–(3)\end{array} \)

Substituting equation (3) in (1), we get-

\(\begin{array}{l}mg=\frac{GMm}{R^{2}}\end{array} \)

Simplifying the above equation, we get

\(\begin{array}{l}g=\frac{GM}{R^{2}}\end{array} \)

Thus, we arrive at the relationship between g and G as –

\(\begin{array}{l}\Rightarrow g=\frac{GM}{R^{2}}\end{array} \)

Physics Related Topics:

Gravity Waves

Relation between Density and Temperature

Relation between Escape Velocity and Orbital Velocity

Relation between Critical Angle and Refractive Index

Universal Law of Gravitation

See the video below to learn about the gravitation

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1. 

   Abhijeet Das December 15, 2020 at 8:21 am

   Keep making the country move in the road of progress. JAI HIND!

   Reply