Topic: Dynamics
Concepts: Cutting strings vs. springs, Newton’s laws, Statics

Solution:

Initially when the blocks are at rest, the tension $T_1$ in the top string holds the weight of both blocks while the tension $T_2$ in the bottom string holds the weight of $m_2$ so

If the top string is cut at the connection point to $m_1$, then at that instant $m_1$ no longer feels an upward tension force. On the other hand, the tension $T_2$ does not change instantaneously since it is sustained in an elastic string (effectively a spring). It takes time for a spring to change its length and we know the tension is determined by its elongation. Thus, we still have $T_2=m_2g$ at that moment.

Applying Newton’s 2nd law to $m_1$,

Applying Newton’s 2nd law to $m_2$,

Thus, the answer is D.