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 two coincides ? A building, a pond, a lake, a mountain ? 

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If the vertical height of the object is very small as compared to the earth's radius, it is called object small, else it is extended.

$(1)$ Building and pond are small objects.

$(2)$ A deep lake and a mountain are examples of extended objects.

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