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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?
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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