FYKOS Year 28 Series 6 Problem 4 — Unbearable weight · FYKOS 28 #28.6.4
Physics · mechanics
Problem
Before the edge of Discworld was reached and overcome and scientific expeditions were made to confirm the existence of the four elephants, turtle and determine its gender some primitve tribespeople thought that the force that kept them on the surface was due to a disc made from a superdense Wasneverwasium. It was truly a very primitive idea because as we know today the expedition, that confirmed the turtle's existence, infamously ended when its boat tore apart and fell or rather did not fall;... Nevertheless we would be interested what kind of surface density would such a disc have to if an object in its middle should experience, while neglecting magical forces, attracted with the same force as the gravitational force on Earth. Assume that, as the legends told, the disc is very thin and is placed ;H=84m=4096m under the surface of Discworld. The Disc should be hmomogeneous and the masses of other bodies negligible. Neglect the movement of the turtle and the elephants. If you haven't read the works of a genius for whom Death came recently then just replace Discworld with Earth. Discworld has a diameter of precisely d=10000km for our purposes.