Problem:1707073: Oscillation

A bob of mass m, suspended by a string of length l₁ 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 l₂, 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 l₁/l₂ is ____. JEE(adv), 2013

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\[The \ initial \ speed \ of \ 1^{st} \ bob \ (suspended \ by \ a \ string \ of \ length \ l_{1}) =\sqrt{5gl_{1}}\]
\[The\ speed\ of \ this\ bob\ at\ highest\ point\ = \sqrt{gl_{1}}\]
When this bob collides with the other bob there speeds will be interchanged.
\[\therefore \sqrt{5gl_{2}} = \sqrt{gl_{1}}\Rightarrow \frac{l_{1}}{l_{2}}=5\]