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 answer is (b).

Explanation:

• When the rod of length lo moves parallel with the speed v, and when the experimenter is at rest, then l = lo1 - v2c2.
• When the observer is traversing with speed v, the rod is at rest and when the observer’s speed is parallel to the rod’s length, then it is shown as l = lo1-v2c2.
• When both the experimenter and the road are moving in the same direction with the same speed, then l = l​o if they move in the opposite directions with the same speed. And, the rod’s length is shown as,

       $I=101-4 v 2 c 2$

       where, v<c​

       As, $1-4 v 2 c 2<1-v 2 c 2$

      Therefore, $101-4 v 2 c 2<101-v 2 c 2<10$

So, in the case when both are travelling in opposite direction, there will be a minimal length.