A bead $$P$$ sliding on a frictionless semi-circular string ($$ACE$$) and it is at point $$S$$ at $$t = 0$$ and at this instant the horizontal component of its velocity is $$v$$. Another bead $$Q$$ of the same mass as $$P$$ is ejected from point $$A$$ at $$t = 0$$ along the horizontal string $$AB$$, with the speed $$v$$, friction between the beads and the respective strings may be neglected in both cases. Let $$t_{P}$$ and $$t_{Q}$$ be the respective times taken by beads P and Q to reach the point B, then the relation between $$t_{P}$$ and $$t_{Q}$$ is