Final answer:
The center of gravity of a person hanging at rest from a vertical rope is directly below where the hands contact the rope, and the tension in the rope is equal throughout its length and directed upwards.
Step-by-step explanation:
When you hang at rest by your hands from a vertical rope, your center of gravity will be directly below the point where your hands contact the rope. Since the body is suspended freely and not moving, the center of gravity aligns with the rope due to the force of gravity acting downward. Concerning the rope's tension, it can be stated that when a weight, such as your body, is suspended freely by a rope, the tension in the rope is directed upwards, opposing the force of gravity. This tension is equal throughout the length of the rope as long as the rope is massless and there are no other forces acting on it, aside from its support and the weight.