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Three balls

Three small identical balls (denoted as $A$, $B$, and $C$) of mass $m$ each are connected with two massless rods of length $\ell$ so that one of the rods connects the balls $A$ and $B$, and the other rod connects the balls $B$ and $C$. The connection at the ball $B$ is hinged, and the angle between the rods can change effortlessly. The system rests in weightlessness so that all the balls lie on one line. The ball $A$ is given instantaneously a velocity perpendicular to the rods.

Find the minimal distance $d$ between the balls $A$ and $C$ during the subsequent motion of the system. Any friction is to be neglected.