Ten bags and one heavy

1. Take k coins from bag k (from 1 to 10) and weigh a single coin.
2. Expected weight if they were all 10 g: 10(1+2+·s+10)=550 g.
3. Final section: If the heavy bag is k, an excess of exactly k grams will appear. The heavy bag is then identified by reading the excess in grams.

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Take $k$ coins from the $k$ bag (from 1 to 10) and make a single weighing.
Expected weight if all were 10 g:

$$ 10(1+2+\cdots+10)=550\text{ g}. $$

If the heavy bag is $k$, an excess of exactly $k$ grams will appear.
Answer: The heavy bag is identified by reading the excess in grams.