FYKOS Year 30 Series 5 Problem 1 — space snowman · FYKOS 30 #30.5.1

Physics · mechanics

Problem

Consider a snowman consisting of 3 homogeneous spheres of density

ρ

with centres on a line, floating in free space. The smallest sphere (the head) has radius

r

and each consecutive sphere has twice the radius of the previous one. Our snowman is the only thing in the universe and it does not rotate in any way. Find the force holding the head to the rest of the snowman. Bonus: Generalise the problem for

N\ge3

spheres. Will the force converge to a finite value for

N→∞

or will it go to infinity?

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