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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 qualitaitve 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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when the vertical height of the object is very small as compared to the earth 's radius , we call the object small ,otherwise it is extended .
(i) Building and pond are small objects.
(ii) A deep lake and a mountain are examples of extended objects .
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