A flexible chain, of length $$L$$ and uniform mass per unit length $$\lambda$$, slides off the edge of a frictionless table as shown. Initially a length $$y=y_0$$ of the chain hangs over the edge, with the chain held at rest. Now the chain is let free. The velocity of the chain when the chain becomes completely vertical, that is when the chain is just to leave the edge, is

A

$$v=\sqrt{g\left(L-\frac{y_0^2}{L}\right)}$$

B

$$v=\sqrt{2g\left(L-\frac{y_0^2}{L}\right)}$$

C

$$v=\sqrt{g(L-y_0)}$$

D

$$v=\sqrt{2g(L-y_0)}$$