A bob of mass m, suspended by a string of length${\text{L}}_1$ , is given a minimum velocity required to complete a full circle in the vertical plane, At the highest point, it collides elastically with another bob of mass m suspended by a string of length ${\text{L}}_2$ which is initially at rest. Both the strings are mass less and inextensible. If the second bob, after collision acquires the minimum speed required completing a full circle in the vertical plane, the ratio ${\text{L}}_2/{\text{L}}_1$ is