Final answer:
The king must avoid using force on Hamlet primarily because Hamlet is well-liked by the people (option B), but his royal ties and emotional distress also contributes to the need for a cautious approach.
Step-by-step explanation:
The king must not put the "strong arm" on Hamlet for several reasons, though the most compelling is that Hamlet is well-liked by the people. This popularity offers him a layer of protection, as any forceful action against him could lead to public dissent and destabilize the kingdom. Additionally, Hamlet's royal blood as a member of the royal family makes him inherently significant and well-connected, which would make it politically risky to handle him with overt aggression.
Furthermore, Hamlet's emotional state is another reason for the king to proceed with caution. His erratic behavior and displays of madness, which might partially be feigned as a strategic front, nonetheless represent a mind grappling with profound moral and psychological dilemmas. This complex emotional turmoil that Hamlet is experiencing makes him unpredictable and potentially volatile. Therefore, the correct option in terms of why the king must not forcefully deal with Hamlet is B) Hamlet is well-liked by the people, although elements of C) and D) also play roles in the broader narrative of the play.