Minimum pumping length of finite language

Question

Background
Let L = {aa}. We know that the minimum pumping length of L is |aa| + 1 = 3. For this length all the three conditions of the pumping lemma vacuously hold true.
Doubt
Let L = {aa, aab}. Is it right to say the minimum pumping length is max(|w| | w belongs to L) + 1(in this case |aab| + 1 = 4) for finite languages?

Answer 1

Let $w \in L$ be the longest string of the finite language $L$. Assume a pumping length $p \leq |w|$. This would imply $w = xyz$ with $|y| \geq 1$ and $xy^2z \in L$. Can you see the contradiction?

Having ruled out pumping length $p \leq |w|$, the minimal possible value for $p$ is indeed $|w|+1$, for which as you noted the conditions of the pumping lemma are trivially true.