A bob of mass m, suspended by string of length $$l_1$$, is given a minimum velocity required to completea full circle in the vertical plane. At the highestpoint,it collides elastically with another bob of mass m suspendedbya string of length $$l_2$$, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio $$\frac{l_1}{l_2}$$ is