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 ‘\( L-l \)’ the other side of the pully. At a certain point of time, when \( l=\dfrac{L}{x} \), the acceleration of the chain is \( \dfrac{g}{2} \). The value of \( x \) is ______.
