FYKOS Year 27 Series 6 Problem 1 — anticore · FYKOS 27 #27.6.1

Physics · mechanics

Problem

There are two homogenous non-rotating planets the shape of perfect sphere's with outer radii

R_{Z}

. The first of which is a perfect sphere with a density of

ρ

a on its surface the gravitational acceleration is

a_{g}

. The second is hollow to half its radius and then its full. If both planets would be out of the same homogenous material, on the surface of which planet shall the gravitational acceleration be greater and what shall be the ratio of the two gravitational accelerations on the two planets? If the gravitational acceleration on the surface of the second planet will be

a_{g}

, what does the density of the second planet have to be?

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