The Centers of Mass (CM) of both dumbbells are stationary. Both are rotating clockwise with angular velocity \( \omega = 2u/l \).
The “outer” particles (which didn’t collide initially) rotate in circles of radius \( l/2 \).

After a rotation of \( \pi \) radians (half a circle), the top tip of Dumbbell A reaches the bottom point (the center line). Simultaneously, the bottom tip of Dumbbell B reaches the top point (the center line).
Thus, the two tips collide at the exact same location where the first collision occurred. This is the second collision.

Just before the second collision:
– Tip of A is moving Left with velocity \( -u \).
– Tip of B is moving Right with velocity \( +u \).
After elastic collision (velocity exchange):
– Tip of A acquires \( +u \).
– Tip of B acquires \( -u \).

Resulting Motion:
For Dumbbell A, both particles now move Right with velocity \( u \). Rotation stops, translation resumes.
For Dumbbell B, both particles move Left.
The dumbbells move away from each other and never return.