simple

         as there is no external force in x direction, the x coordinates of the com will be the same throughout. but in y axis we have g force and N force as external force. thus the centre of mass will move in y direction. so y coordinate constantly changes. so answer is (a) and (c). c is true as we can check it by applying cons. of mom. in x axis. the com is the only point whose dist. from the ring is fixed and also falls vertically..Y coordinate changes, X coordinate is const.

  

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