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

`(5)`

Explanation

The initial speed of 1st bob (suspended by a string of length `l_1`) is `sqrt(5gl_1)`.
The speed of this bob at height point will be `sqrt(gl_1)`
When this bob collides with the other bob there speeds will be interchanged.
`sqrt(gl_1)=sqrt(5gl_1)impliesl_1/l_2=5`