1. An apparatus having dual modes adapted to control the position of a cursor on a display screen comprising: a ball capable of being rotated to determine said cursor position; a roller device in contact with said ball to detect said rotation of said ball; a shell having thereon a first opening through which said ball protrudes, the shell adapted to accommodate therein said ball and said roller device, the shell including a room; and a cover connected to said shell and disposed in said room, the cover extractable from said room to shield said ball from being inadvertently contacted, the cover retractable into said room to permit said ball to be contacted and used.