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 quantitative meaning of 'small' and 'extended' in this regard? For whicih of the following the two coincides? A building, a pond, a lake, a mountain??

The centre of mass of an extended body on the surface of the earth and its centre of gravity

An object of mass m is raised from the surface of the earth to a heigt equal to the radius of the earth , that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy?

A small magnet of magnetic moment M is placed at broad side on position of a magnet of magnetic M', length 2l' in such a way that the axis of former coincides with the perpendicular bisector of the latter. The separation between their centres is d. Calculate the nature of interaction (force or couple ) among them. What is its limiting value, when d becomes very large ?