A ball rotates at a rate $r$ rotations per second and simultaneously revolves around a stationary point $O$ at a rate $R$ revolutions per second $(R<r)$.The rotation and revolution are in the same sense.A certain point on the ball is in the line of the centre of the ball and point $O$ at a certain time.This configuration repeats after a time

$(1)\frac{1}{r-R}$

$(2)\frac{1}{R}-\frac{1}{r}$

$(3)\frac{1}{r+R}$

$(4)\frac{1}{R}+\frac{1}{r}$