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 $I=\frac{L}{x}$, the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is.