Draw a graph showing the variation of acceleration dur to gravity g with distance r from the centre of the earth.

For points located outside the Earth, the acceleration due to gravity decreases with distance. It is inversely proportional to the square of the distance from the center of the Earth, meaning as one moves further away, gravity becomes weaker. Specifically, this means that the gravitational force felt at a height above Earth’s surface diminishes with increasing distance from the center.

In contrast, for points inside the Earth, gravity behaves differently. The acceleration due to gravity decreases linearly as one moves closer to the center. This indicates that the gravitational pull inside the Earth is directly related to the distance from the center.

For points lying onside the earth (r > R)
gₕ/g = R²/(R + h)² = R²/r² or gₕ = gR²/r²
gₕ ∝ 1/r²

For points lying inside the earth (r < R)
gₔ = g(R – d)/R = gʳ/R or gₔ = gʳ/R
gₔ ∝ r