Where is my Centre of Mass?

Suppose there is a ball moving along a parabola. After a certain duration, it breaks up into 2 parts because of some internal stress. The 2 parts go on two different parabolic paths because the velocities of the parts changed at the instant of breaking. You locate the 2 parts at some instant t and calculate the position of the centre of mass of the combination at that instant.

Will the centre of mass be found at the same point on the original parabola where the centre would have been if the ball had remained intact?

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