If the Earth were flat...

There was a time, long ago, when people thought that the Earth was flat. Let us suppose that the Earth is a flat disk with density $$\rho=5.5\times 10^{3}~\text{kg}/\text{m}^3$$. The acceleration due to gravity, right at the surface of the planet, and close to center of the disk is $$g=9.8~\text{m}/\text{s}^2$$. Determine the thickness $$h$$ in kilometers of the disk. You may assume that $$h\ll R$$, where $$R$$ is the radius of the disk.

Details and assumptions

The universal gravitational constant is $G=6.67\times 10^{-11}~\text{m}^{3}\text{kg}^{-1} \text{s}^{-2}$

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