Exam-style question
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If two observers measure the length of a moving rod, which observer will measure the longer length?.
- A.The observer for whom the rod is at rest
- B.The observer for whom the rod is moving
- C.Both observers will measure the same length
- D.The observer who measures the rod's speed as zero
Model answer
What a good answer should say
- The observer for whom the rod is at rest
Explanation
Why this works
Formula/rule: In the rod’s rest frame the length is its proper length L0. In any other frame where the rod moves, the length is L = L0 sqrt(1 - v^2/c^2) < L0.
Substitution: Since sqrt(1 - v^2/c^2) < 1, the moving observer measures a shorter length. Working: Thus the rest observer measures the longer length.
Answer: The observer for whom the rod is at rest. Units/conclusion: Lengths are in metres (m).
Common mistake
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