The centre of mass of an extended object is:

Question

BlackTom AI · Accepted Answer

Question: The centre of mass of an extended object is:

Option 1: the weighted average position of the object's mass.
This is correct in general. The centre of mass is the point where you can balance the object, and it represents the average position of all the mass when each part of the object contributes proportional to its mass. For continuous bodies, this is computed as a mass-weighted average over the volume (or area in two dimensions).

Option 2: the geometric centre of the object.
This is often incorrect. The geometric centre (or centroid) depends only on shape and geometry, not on how mass is distributed. If the object has nonuniform density, the centre of mass shifts away from the geometric centre toward regions with more mass. Only for a perfectly uniform density and symmetric shape do the geometric centre and centre of mass coincide; otherwise they differ.

Option 3: the point on the object that feels heaviest.
This is a misconception. The centre of mass is not the location of the maximum weight felt at a single point on the surface. It is a global property determined by all mass elements. The point that feels heaviest when you press on the object does not define the centre of mass, and in many cases will not coincide with it.

Option 4: always located within the material of the object.
This is not always true. For some shapes with mass distributed around a ring or about a hollow center (such as a thin hoop or a circular ring with uniform mass), the centre of mass can lie at the geometric center, which in these cases is not within material (it’s in empty space). Therefore, the centre of mass is not guaranteed to lie inside the material itself.

In summary, the accurate description among the options is that the centre of mass is the weighted average position of the object's mass, reflecting how mass is distributed throughout the object.

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