5. Two dumbbells, consisting of weightless rods of length $2 L$ and identical small balls, slide towards each other with the same speed $V$ as shown in the figure. Describe the motion of the dumbbells after the collision of the balls in two cases: A) the collision is perfectly elastic; B) the collision is perfectly inelastic.
Solution. When any two balls collide, the velocities of the others do not change, as the collision is instantaneous. In a perfectly elastic collision of two identical balls, they exchange velocities. Therefore, each dumbbell will begin to rotate around its center with an angular velocity of $\frac{V}{L}$. After half a period, the balls that did not participate in the first collision will end up at the initial collision point (neglecting the radii of the balls). After the second perfectly elastic collision, the dumbbells will diverge, maintaining the translational nature of the motion and the speed.

In the case of a perfectly inelastic collision, the touching balls will stick together and become stationary. The system will begin to rotate around this point with an angular velocity of $\frac{V}{2 L}$.

Answer: A) they will diverge, maintaining their initial speeds;

B) they will begin to rotate with an angular velocity of $\frac{V}{2 L}$.

Criteria: 20 points - correct and justified solution (possibly different from the one above); 15 points - solution with insufficient justification; 10 points - generally correct solution, but quantitative characteristics are not specified; or in the perfectly elastic collision, the second collision is not taken into account; $\mathbf{5}$ points - correct solution of one of the points; or a solution in which the main effects are taken into account, but some errors are made; $\mathbf{0}$ points - everything else.