Pick a Sack

Arrange all the sacks in one line and number it $1,2,3....,n$ . Now take $1$ grain from $1st$ sack, $2$ grains from $2nd$ sack and so on.

Now if all the sack would have contained $10 grams$ grains then, weight would have been - $10*(1+2+3+4.... +n) = 10*\{ \frac{n(n+1)}{2}\}$

but actually weight that we will get is - $10*1+10*2....+ 9*k .... +10*n = 10*1+10*2....+ 10*k -k .... +10*n = 10*\{ \frac{n(n+1)}{2}\} -k$

Now, on subtracting the weight that we calculated earlier and the weight that we got, we see that we are left with $k$ which is the sack number. So only once the weighing machine was used.