Topic: Rigid Bodies
Concepts: Artificial gravity, Conservation of angular momentum

Solution:

Let $\omega$ be the initial angular velocity of the space station. In the rotating frame, all objects experience a (fictitious) centrifugal force of magnitude $ma_c=m\omega^2r$ which looks like gravity $mg$ if we have

After two astronauts climb into the center, the space station rotates at angular velocity $\omega’$ so the artificial gravity becomes $g’=\omega’^2r$. We can find $\omega’$ by conserving angular momentum since no external torque acts on the space station.

We have

Since $L_i=L_f$,

Finally,

so the answer is E.