To simplify the given expression \(\sqrt{2a^2} \cdot \frac{(1-a)^2}{\sqrt{50}}\) where \(a > 1\), let's break it down step by step.

1. **Simplify \(\sqrt{2a^2}\):**
\[
\sqrt{2a^2} = \sqrt{2} \cdot \sqrt{a^2} = \sqrt{2} \cdot a
\]

2. **Simplify \(\sqrt{50}\):**
\[
\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}
\]

3. **Substitute these simplified forms back into the original expression:**
\[
\sqrt{2a^2} \cdot \frac{(1-a)^2}{\sqrt{50}} = (\sqrt{2} \cdot a) \cdot \frac{(1-a)^2}{5\sqrt{2}}
\]

4. **Simplify the expression further:**
\[
(\sqrt{2} \cdot a) \cdot \frac{(1-a)^2}{5\sqrt{2}} = a \cdot \frac{(1-a)^2}{5}
\]

5. **Combine the terms:**
\[
a \cdot \frac{(1-a)^2}{5} = \frac{a(1-a)^2}{5}
\]

So, the simplified form of the given expression is:
\[
\frac{a(1-a)^2}{5}
\]