The centre of mass of an extended body on the surface of the earth and its centre of gravity
Centre of mass of any object is described as mean position of mass in the object. Many objects with uniform shape and mass distribution have their centre of masses at their centre
Whereas centre of gravity of the object is the point where the gravity is assumed to act i.e. when the object is suspended from a fixed point, the torque of gravity about the point is zero.
Centre of mass and centre of gravity are not same points for an extended body with large dimensions due to different mass distribution. But if the size of the body is less and the gravitational field is uniform, then the centre of gravity and centre of mass are nearly at the same point.
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