Problem 1.353

The rod $A^{\prime} B^{\prime}$ moves with a constant velocity $v$ relative to the rod $A B$ (Fig. 1.91). Both rods have the same proper length $l_{0}$ and at the ends of each of them clocks are mounted, which are synchronized pairwise: $A$ with $B$ and $A^{\prime}$ with $B^{\prime}$. Suppose the moment when the clock $B^{\prime}$ gets opposite the clock $A$ is taken for the beginning of the time count in the reference frames fixed to each of the rods. Determine: (a) the readings of the clocks $B$ and $B^{\prime}$ at the moment when they are opposite each other; (b) the same for the clocks $A$ and $A^{\prime}$.