FYKOS Year 29 Series 2 Problem 2 — numismatic · FYKOS 29 #29.2.2

Physics · mechanics

Problem

Once in a while, a situation may occur, that the nominal value of coins is lower that their manufacturing costs. Assume we have two coins, made of a gold-silver alloy. The first one has diameter

d_{1}=1\;\mathrm{cm}

, second one

d_{2}=2\;\mathrm{cm}

, both have thickness

h=2\;\mathrm{mm}

. If we submerge them in mercury, the smaller one sinks to the bottom, whilst the larger one rises to the surface. If we submerge both coins, smaller one on top of the larger, they neither rise nor sink. Assuming the smaller coin is made of pure gold, determine the fraction of silver in the larger coin (in percent of mass). Bonus: How would the result change if the smaller one could contain silver as well?

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