Question

A bob of mass $m$, suspended by a string of length $l_1$ 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 $l_2$, 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 $l_1/l_2$ is :

Answer 1

The initial speed of 1st bob (suspended by a string of length $l_1$)is $\sqrt{5g{l}_1}$ .
The speed of this bob at highest point will be $\sqrt{g{l}_1}$ .
When this bob collides with the other bob their speeds will be interchanged.
$\sqrt{g{l}_1}=\sqrt{5g{l}_2}\Rightarrow \frac{l_1}{l_2}=5$