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 \(A^{\prime}\).