A particle of mass $m$ is suspended from a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that $r = \frac{L}{\sqrt{2}}$. The speed of particle will be:
(1) $\sqrt{rg}$
(2) $\sqrt{2rg}$
(3) $\sqrt{\frac{rg}{2}}$
(4) $2\sqrt{rg}$