A rod of length `l=2m` is maintained to rotate with a constant angular velocity `omega=1 rad//s` about vertical axis passing through one end (fig). There is a spring of spring constant `k=1 N//m` which just encloses rod inside it in natural length. One end of the spring is attached to axis of rotation. `S` is sleeve of mass `m=1kg` which can just fix on rod. All surfaces are smooth. With what minimum kinetic energy (in `J`) sleeve should be projected so that it enters on the rod without impulse and completely compresses the spring.

Answer

6