Question

establish relation between 'g' and 'G '

Answer 1

G stands for Newton's universal gravitational constant, whereas gstands for the acceleration due to gravity at a certain point. ... (According to Newton's law of universal gravitation the force of attraction between two bodies is given by F = GMm/r 2, where the symbols stand for their usual well known meanings.

Answer 2

Question

Establish relation between 'g' and 'G '

Answer

Before we establish a Relation between 'G' and 'g', lets see what these symbols stand for.

'G' - Expression for Universal Gravitational Force.

'g' - Acceleration due to gravity.

If we establish an expression for these two values, it would probably be an equation for Acceleration due to Gravity.

Relation between 'g' and 'G'

Now, lets form a relation between 'G' and 'g' taking the example of the Object on an Earth.

Let 'M' be the mass of the Earth.

Let 'R' be the radius of the Earth.

If we drop a body of mass 'm', the force exerted by the earth on the body is given by Newtons Law of Gravitation or Universal Law of Gravitation.

This force produces an acceleration [g] on the body of mass [m].

According to Newtons 2nd Law of Motion,

F = mg  ---> 1

ie,

F = $\mathsf{\frac{GMm}{R^{2}}}$---> 2

From 1 and 2,

mg = $\mathsf{\frac{GMm}{R^{2}}}$

['m' and 'm' gets cancelled]

⇒ g = $\mathsf{\frac{GM}{r^{2}}}$

↓ Remember ↓

The value of 'G' does not depend upon the mass of the body. It changes slightly from place to place. But for most of the purposes it is takes as 9.8 m/s²