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QPage 458: Q5: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Page 458: Q5 Solution: An aeroplane travels over a rectangular field 100 m _ 50 m,…

An aeroplane travels over a rectangular field 100 m _ 50 m, parallel to its length. What should be the speed of the plane so that the field becomes square in the plane frame?

Step-by-Step Verified Solution

**Answer:** v=32c≈0.866cv = \frac{\sqrt{3}}{2}c \approx 0.866c. **Step-by-Step Explanation:** The field is 100×50100 \times 50 m. For it to appear square, the length along the direction of motion must be contracted from 100 m to 50 m.
50=1001−v2/c2⇒1−v2/c2=0.5⇒v2/c2=0.75⇒v=32c50 = 100\sqrt{1 - v^2/c^2} \Rightarrow \sqrt{1 - v^2/c^2} = 0.5 \Rightarrow v^2/c^2 = 0.75 \Rightarrow v = \frac{\sqrt{3}}{2}c

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