The relation between G and g with equation

Last updated on April 14th, 2021 at 05:19 pm

This post highlights the relation between G and g. G is the universal gravitational constant and g is the acceleration due to gravity. So let’s find out the relationship in terms of an expression or equation.

Relation between G and g

Let’s consider an apple of mass m falling from a tree. The apple is acted upon by gravitational force due to earth, and therefore, it is attracted to the earth.

From Newton’s law of gravitation, the gravitational force acting on the apple is given by,
F =GMm/R² …………. (1)
where M is the mass of the earth and R is the radius of the earth.

From Newton’s second law, the apple is accelerated towards the centre of the earth due to
gravitational force.
hence, we can write F =mg …………………(2)

Now, from equation (1) and (2), we get
mg = GMm/R²

=> g = GM/R²

This equation shows the relationship between g and G. From this equation we can see that g is independent of mass of the falling body, i.e., all bodies irrespective of their masses are accelerated to the same extent due to gravity.

Now use this formula and find out the value of g mathematically here.