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Assuming it has been lifted straight up, to a height of "h" over the table, the center of mass would be at a height "h/4" over the table. The reasoning is as follows: You can divide the rope into two halves, the half that is lifted up (which has a center of mass of "h/2"), and the half that is still on the table (which has a center of mass of 0). Take the average of both, since both parts have the same weight (or mass).

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