A

Step 1: In a vacuum, there is no air resistance acting on the objects. Therefore, the only force acting on an object during free fall is the gravitational force.
Step 2: According to Newton's second law of motion, the acceleration of any object is given by the equation:
$$ F = ma $$
where $F$ is the net force, $m$ is the mass, and $a$ is the acceleration.
In this case, the only force is the gravitational force which can be expressed as:
$$ F = mg $$
where $g$ is the acceleration due to gravity.
Step 3: Since both balls are released from the same height and are in free fall, according to Galileo's principle, all objects fall with the same acceleration regardless of their mass when air resistance is negligible.
Conclusion: Therefore, the acceleration due to gravity in a vacuum is the same for both the iron ball and the wooden ball, which is approximately $9.81 ext{ m/s}^2$.
Hence, the correct answer is option A.