Exam-style question
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If a spaceship travels at 0.9c, what is the relationship between its proper length L0 and observed length L?.
- A.L = L0 / √(1 – v²/c²)
- B.L = L0 √(1 – v²/c²)
- C.L = L0 (1 + v²/c²)
- D.L = L0 (1 – v²/c²)
Model answer
What a good answer should say
- L = L0 √(1 – v²/c²)
Explanation
Why this works
Formula/rule: L = L0 √(1 – v²/c²). Substitution: v = 0.9c, so v²/c² = 0.81.
Working: √(1 – 0.81) = √0.19 ≈ 0.435. Answer: L ≈ 0.435 L0.
Units/conclusion: The observed length is about 43.5 % of the proper length, demonstrating length contraction.
Common mistake
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