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QPage 457: Q4: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Page 457: Q4 Solution: An experimenter measures the length of a rod. In the cases…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat the observer’s speed relative to the lab as the relevant quantity for length contraction, or they compute the relative speed as a simple difference or sum of velocities. In special relativity the contraction factor is $gamma(v_{ ext{rel}})=1/sqrt{1-(v_{ ext{rel}}/c)^2}$, where $v_{ ext{rel}}$ is the relativistic relative velocity given by $(v_1+v_2)/(1+v_1v_2/c^2)$ for opposite directions. Using the wrong relative speed leads to an incorrect ordering of the measured lengths.

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?

Multiple Choice Options

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

Step-by-Step Verified Solution

**Answer:** (b) The rod and the experimenter move with the same speed v in opposite directions. **Step-by-Step Explanation:** The relative speed is highest when they move in opposite directions, giving the minimum length.

All Questions in this Chapter

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