Question

Earth is considered to have its mass concentrated at its point centre then why does acc^{​​​​n}​​​ due to gravity decrease while we go deeper inside the earth?

Answer 1

The gravitational force is given by F = GmM/r^2
(r^2 denotes "r squared)
Where G is the universal gravitational constant
m is the object mass
M is the planet mass
r is the distance from the centre of the planet.

Since F = mg, where g is the graviational acceleration this gives
g = GM/r^2
whish is independent of the object mass

However, this relation, where M is the total planet mass is only true if you are outside the planet's radius. If you dig a hole, you approach the centre more closely, but now there is a shell of mass that should be ignored (the sum of all the forces from this shell will always be zero).

The mass now inside the radius falls off with a factor (r/R)^3 since it is determined by the relative volume described by your distance from the planet centre r, and the planet radius R.

This gives a relation for the gravitational acceleration at a general radius r < R.

g = GMr/R^3

R, M and G are constants....so g increases with r, and hece decreases as you approach the centre of the earth.