The artificial sweetener used in diet coke is hundreds of times sweeter per unit volume than regular sugar. Classic coke has about 11 teaspoons of sugar in each can which are taken up by water in the diet coke can.
Since sugar is more dense than water, the diet coke will be less dense than classic coke.
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According to Wikipedia:
"Since 1985 in the U.S., Coke has been made with high fructose corn syrup, instead of sugar glucose or fructose, to reduce costs."
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