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Q. Assertion : At the centre of earth a body has centre of mass, but no centre of gravity.
Reason : This is because $g = 0$ at the centre of earth.

AIIMSAIIMS 2013

Solution:

At the centre of earth, $g=0$
$\therefore $ A body has no weight at the centre of earth. and hence no certre of gravity But centre of mass of a body is not related to gravity. So. centre of mass exist