Question

An experimenter measures the length of a rod. In the cases listed, all motions are with respect to the lab and parallel to the length of the rod. In which of the cases the measured length will be minimum?

• A. The rod and the experimenter move with the same speed v in the same direction.
• B. The rod and the experimenter move with the same speed v in opposite directions.
• C. The rod moves at speed v but the experimenter stays at rest.
• D. The rod stays at rest but the experimenter moves with the speed v.

Answer 1

The correct option is B The rod and the experimenter move with the same speed v in opposite directions.

The rod and the experimenter move with the same speed v in opposite directions, as if a rod is moving with speed parallel to its length, and when the rod and the experimenter move with the same speed $\nu$ in opposite direction the new $\nu$ will be $2\nu$, as the velocity adds up and hence the length will be minimum in this case.