Step 1: Find Ka first:
$K_a = c\alpha^2 = 0.05 \times (0.04)^2 = 0.05 \times 0.0016 = 8 \times 10^{-5}$.
Step 2: Use Ka at the new concentration:
$\alpha_2^2 = K_a/c_2 = 8\times10^{-5}/0.1 = 8 \times 10^{-4}$.
Step 3: Take the root:
$\alpha_2 = \sqrt{8\times10^{-4}} = 0.02828$, which is 2.828%.
Step 4: Trend check:
More concentrated acid dissociates to a smaller fraction, so 2.828% being less than 4% is correct.
Final Answer:
The percent dissociation is 2.828%, option (C).
\[ \boxed{2.828\%} \]