A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length 'l' is hanging on one side and rest of its length 'L - l' is hanging on the other side of the pulley. At a certain point of time, when $l\mathit{ }\mathit{=}\mathit{ }\frac{\mathit{L}}{\mathit{x}}$, the acceleration of the chain is $\frac{\mathit{g}}{\mathit{2}}$. The value of x is .......