Harry Potter is sitting $2.0$ meters from the center of a merry-go-round when Draco Malfoy casts a spell that glues Harry in place and then makes the merry-go-round start spinning on its axis. Harry has a mass of $\text{50.0 kg}$ and can withstand $\text{5.0} \ g\text{'s}$ of acceleration before passing out. What is the magnitude of Harry's angular momentum when he passes out?

(A) $\text{200 kg} \cdot \text{m}^2\text{/s}$
(A) $\text{330 kg} \cdot \text{m}^2\text{/s}$
(A) $\text{660 kg} \cdot \text{m}^2\text{/s}$
(A) $\text{1000 kg} \cdot \text{m}^2\text{/s}$
(A) $\text{2200 kg} \cdot \text{m}^2\text{/s}$
1. **Identify the centripetal acceleration**: Harry can withstand an acceleration of \(5.0 \, g\), where \(g = 9.8 \, \text{m/s}^2\). Therefore, the maximum centripetal acceleration \(a_R\) Harry can withstand is:
   \[
   a_R = 5.0 \times 9.8 \, \text{m/s}^2 = 49 \, \text{m/s}^2
   \]

2. **Relate centripetal acceleration to angular velocity**: The centripetal acceleration \(a_R\) is given by:
   \[
   a_R = \omega^2 r
   \]
   where \(\omega\) is the angular velocity and \(r\) is the radius (distance from the center of the merry-go-round). Given \(r = 2.0 \, \text{m}\), we can solve for \(\omega\):
   \[
   \omega^2 \cdot 2.0 \, \text{m} = 49 \, \text{m/s}^2
   \]
   \[
   \omega^2 = \frac{49 \, \text{m/s}^2}{2.0 \, \text{m}} = 24.5 \, \text{rad}^2/\text{s}^2
   \]
   \[
   \omega = \sqrt{24.5} \, \text{rad/s} \approx 4.95 \, \text{rad/s}
   \]

3. **Calculate the moment of inertia**: For a point mass, the moment of inertia \(I\) is given by:
   \[
   I = mr^2
   \]
   where \(m = 50.0 \, \text{kg}\) and \(r = 2.0 \, \text{m}\). Thus:
   \[
   I = 50.0 \, \text{kg} \cdot (2.0 \, \text{m})^2 = 50.0 \, \text{kg} \cdot 4.0 \, \text{m}^2 = 200 \, \text{kg} \cdot \text{m}^2
   \]

4. **Calculate the angular momentum**: The angular momentum \(L\) is given by:
   \[
   L = I \omega
   \]
   Substituting the values of \(I\) and \(\omega\):
   \[
   L = 200 \, \text{kg} \cdot \text{m}^2 \cdot 4.95 \, \text{rad/s} \approx 990 \, \text{kg} \cdot \text{m}^2/\text{s}
   \]

5. **Compare with the given options**: The closest option to our calculated value is \(1000 \, \text{kg} \cdot \text{m}^2/\text{s}\).

The final answer is \(\boxed{1000 \, \text{kg} \cdot \text{m}^2/\text{s}}\).