Question

Define Acceleration due to gravity. Derive an mathematical expression of g = GM/R?
where G and M are Gravitation constant and Mass of an object.​

Answer 1

Explanation:

The gravity of Earth, denoted by g, is the net acceleration that is imparted to objects due to the combined effect of gravitation and the centrifugal force.

Weight of an object on Earth = Gravitational force exerted on an object by the Earth.

Let us consider a body having mass "m".

mg=G⋅mMR2

where,

g=acceleration due to gravity,

G=Gravitational constant,

M=Mass of the Earth,

and R=radius of the Earth.

Weight of the body (on Earth)=

mass(m)⋅gravitational acceleration(g)

Cancel out the m on both sides to get:

g=G⋅MR2=GMR2