The centre of gravity of a body on the earth coincides with its centre of mass for a ‘small’ object whereas for an ‘extended’ object it may not. What is the qualitative meaning of ‘small’ and ‘extended’ in this regard? For which of the following the two coincides? A building, a pond, a lake, a mountain?

The geometric centre of gravity is the geometric centre, but the mass of the place where the complete mass of the body is considered is the mass of the centre of mass. When an object’s vertical height is close to the earth’s surface, it is considered to be tiny. The item is said to be stretched if the distance between it and the earth’s surface is great.

A building and a pond are little objects, whereas a mountain and a lake are considered extended objects.