An experimenter measures the length of a rod. In the scenarios provided, all motions are relative to the lab and parallel to the rod's length. In which scenario will the measured length be minimum?

Step-by-step solution

The measured length of a rod is given by L = L₀ 1 - u^2 c^2 , where L₀ is the proper length and u is the relative speed between the rod and the observer. The measured length is minimum when the relative speed u is maximum. In scenario (1), the relative speed is u = v . In scenario (2), the relative speed is u = 0 . In scenario (3), the relative speed is u = v . In scenario (4), the rod and the experimenter move in opposite directions. The relative speed is given by the relativistic velocity addition formula: u = v