A model of Earth's interior: Look up the radius and mass of the Earth.

Radius is 6,371 km

Mass is 5.974 x 10^24 kg

Calculate its average density.

p_e = (5.974 x 10^24 kg)/ (4/3)pi r^3 = (5.974 x 10^24 kg)/ (4/3)pi (6371)^3 = 5.54 g/cm^3

Imagine a planet of the same radius made completely and uniformly out of an incompressible fluid such that its mass density is equal to the average density of the Earth.

Find how the acceleration of gravity depends on the distance from the center of the planet. Sketch a graph showing this dependence.

I know the dependence would be a straight line but i'm not sure how to prove in mathematically

Now, use the equation of hydrostatic equilibrium to find the pressure as a function of distance from the center. What is the pressure at the center of the planet?