Answer
As the soda drains out of the can, the value of $h$ will gradually decrease below $6.0~cm$ and then gradually increase back up to $6.0~cm$
Work Step by Step
By symmetry, when the can is full, the height of the center of mass is half of the can's total height. The center of mass of the full can is $6.0~cm$
By symmetry, when the can is empty, the height of the center of mass is half of the can's total height. The center of mass of the empty can is $6.0~cm$
As the soda drains out, the center of mass of the soda becomes lower while the center of mass of the metal can (not including the soda) remains at a height of $6.0~cm$
Therefore, the value of $h$ will decrease initially when the soda starts to drain out.
As more soda drains out, the center of mass of the soda will continue to become lower, however, because the mass of the remaining soda also decreases, there will be a moment when $h$ starts to rise higher.
Finally, when all the soda drains out of the can, the value of $h$ will be $6.0~cm$
In summary, as the soda drains out of the can, the value of $h$ will gradually decrease below $6.0~cm$ and then gradually increase back up to $6.0~cm$
