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 $\frac{l_1}{l_2}$ is

Answer 1

Speed of first bob at highest point $=\sqrt{g{l}_1}$
For elastic collision between objects of same mass, velocities are exchanged $\Rightarrow$ speed of $2^{nd}$ bob $=\sqrt{g{l}_1}$ but $\sqrt{g{l}_1}=\sqrt{5g{l}_2}$
$\Rightarrow \frac{l_1}{l_2}=5$