Acceleration due to gravity at the centre of earth

Hi!

Leaving behind everything, lets start from the start and answer your question.

So, First of all,

What is gravitation or gravitational force & acceleration due to gravity ?

Many people get confused between gravitational force and acceleration due to gravity. Let me make it clear to you at first that they both are different. Gravitation is a force (S.I. Unit is Newton (N)) and acceleration due to gravity is acceleration (S.I. Unit is m/s²). They both are different things at all!

→Gravitation is a force that exists between any two matters (masses).

→Acceleration due to gravity is acceleration produced in a freely falling body in vacuum.

In the above lines, the term free fall is used.

What is free fall?

A object is said to be freely falling if it's moving towards the center of a planet only by the gravitational force of the planet and no other force is acting upon the object- not even air resistance.

Acceleration due to gravity on earth on an average is always 9.8 m/s².

Here, the term on an average is used because acceleration due to gravity (g) is equal to (G*M)/(R)² , where G is the universal gravitation constant, M is the mass of the planet and R is the radius of the planet(we'll not go into that details....); and since the earth is not a perfect sphere, the radius varies at the equator and the poles, and, hence, the value of g (acc. due to gravity) also varies.....

In the above paragraph, it is said that :

The value of universal gravitation constant (G) is defined in newton's universal law of gravitation and it's value is  N ms² / kg ².

Since, g = Gm/r² , if radius is increased, the value of g will decrease and vice-versa.

Now, read the last paragraph very carefully.........

If an object is placed above the surface of the earth, The value of g will be less than 9.8 m/s². Now, you will think that if an object is placed under the surface of the earth, the value of g will increase. But, this is false. It will still decrease. And, at the core (center of the earth), it's value will be 0 m/s².