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Me = 4/3 π Re³ * d, where Re = Radius of Earth

Me = Mass of EArth d = density of Earth (we assume it is uniform)

Let us find the gravity at a distance r from the center of Earth. Mass of Earth enclosed inside the radius r is :

M = 4/3 π r³ d = 4/3 π r³ (3Me /Re³ 4π)

= Me r³/ Re³

Gravity at a location r distance away from center of Earth is = G (Me r³/Re³) / r²

Thus

where g = acceleration due to gravity at the surface of Earth.

Thus

In other words,

Me = Mass of EArth d = density of Earth (we assume it is uniform)

Let us find the gravity at a distance r from the center of Earth. Mass of Earth enclosed inside the radius r is :

M = 4/3 π r³ d = 4/3 π r³ (3Me /Re³ 4π)

= Me r³/ Re³

Gravity at a location r distance away from center of Earth is = G (Me r³/Re³) / r²

Thus

*g' = G Me r / Re³ = g r /Re ,*where g = acceleration due to gravity at the surface of Earth.

Thus

**if r = 0, g' = 0.**In other words,

**. Thus g is proportional to R inside the Earth's surface.***M varies as cube of R and in the denominator, we have a square of R*