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 a 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 `1^(st)` bob (suspended by string of length `l_1`) is `sqrt(5 gh)` .
The speed of this bob at highest point will be `sqrt(gl_1)` .
When this bob collides with the other bob, their speeds will be interchanged.
`sqrt(gl_1) = sqrt(5 gl_2) implies (l_1)/(l_2) = 5` .