The part of the brain that controls posture and balance of the body is the cerebellum.
Explanation: The cerebellum is responsible for coordinating muscle movements, maintaining balance, and posture.
Key points about the other options:
Cerebrum:
The cerebrum is the largest part of the brain and is responsible for higher functions like thought, language, and memory. It is not directly involved in posture and balance.
Medulla:
The medulla is part of the brainstem and controls vital functions like breathing and heart rate. It is not involved in posture or balance.
Pons:
The pons is also part of the brainstem. It plays a role in several functions including sleep, respiration, and facial expressions. It is not primarily responsible for posture and balance.