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 '…

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