Exam-style question
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Which equation correctly represents length contraction in special relativity?.
- A.L = L0 / sqrt(1 - v^2/c^2)
- B.L = L0 sqrt(1 - v^2/c^2)
- C.L = L0 sqrt(1 + v^2/c^2)
- D.L = L0 (1 - v^2/c^2)
Model answer
What a good answer should say
- L = L0 sqrt(1 - v^2/c^2)
Explanation
Why this works
Formula/rule: The Lorentz contraction formula is L = L0 sqrt(1 - v^2/c^2). Substitution: For any speed v < c, the term under the square root is less than 1, so sqrt(1 - v^2/c^2) < 1.
Working: Thus L = L0 × (a factor < 1) gives a length shorter than L0. Answer: L = L0 sqrt(1 - v^2/c^2).
Units/conclusion: The contracted length is measured in metres (m) and is always less than the proper length.
Common mistake
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