Final answer:
The center of mass is the average location where an object's mass is considered to be concentrated and it is usually located at the geometric center for symmetrical objects in a uniform gravitational field.
Step-by-step explanation:
The question pertains to identifying the possible location of the object's center of mass (also referred to as the center of gravity) using given data points. The center of mass is the point where the mass of an object is considered to be concentrated and it plays a key role in the object's rotational inertia and angular momentum. In most situations on Earth, where the gravitational field is considered uniform, the center of mass and the center of gravity are effectively at the same location. When calculating the center of mass, one would typically use vectors representing the position and mass of the individual components within the object, and compute the weighted average of these vectors. The result of this calculation indicates the position vector of the center of mass.
In the case of symmetrical objects like a cone or uniform stick, there are specific points at which the center of mass can be determined using geometrical reasoning and knowledge of the object's shape. For example, the center of mass of a cone can be located by finding the weighted average position taking into account its uniform density, radius, and height. Similarly, the center of mass of a uniform stick is located at its midpoint. Using the given data points and considering the object's shape or symmetry, one can pinpoint the likely location for the center of mass.