Topic: System of Masses
Concepts: Conservation of angular momentum, Conservation of linear momentum, Dynamics of CM

Solution:

Since there are no external forces (and torques), we have conservation of linear momentum and angular momentum. The initial linear momentum is

Since $p_{\text{tot}}=M_{\text{tot}}v_{\text{CM}}$, this means $v_{\text{CM}}=0$ so the CM stays at rest at its initial location $(1, 0)$. Choosing $(1, 0)$ as our axis of rotation, the initial angular momentum is

going counterclockwise. We now go through the possible choices:

• A) Not correct because the CM moved to $(0, 0)$.
• B) Not correct because the linear momentum is nonzero.
• C) Not correct because the angular momentum decreased (since the moment arm decreased by a factor of $\sqrt{2}$).

• D) Not correct because the angular momentum increased (since the moment arm increased by a factor of $2$).

• E) Correct since linear momentum and angular momentum are conserved and the CM stayed at rest.

Thus, the answer is E.