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QPages 456-457: Q3: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Pages 456-457: Q3 Solution: An object may be regarded to be at rest or in motion depending…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often forget that a length must be measured by recording the positions of the rod’s ends at the same instant *in the observer’s own frame*; neglecting this relativity of simultaneity leads to the mistaken belief that both frames see the same contracted length or that the rod physically shrinks.

An object may be regarded to be at rest or in motion depending on the frame of reference chosen to view the object. Because of length contraction it would mean that the same rod may have two different lengths depending on the state of the observer. Is this true?

Step-by-Step Verified Solution

**Answer:** Yes, it is true that the same rod may have different lengths depending on the observer's state of motion. **Step-by-Step Explanation:** According to the special theory of relativity, length is not an absolute quantity. The length of a rod measured in a frame in which it is at rest is called its **proper length** (L0L_0). In a frame in which the rod is moving with speed vv along its length, the measured length is:
L=L01−v2c2L = L_0\sqrt{1 - \frac{v^2}{c^2}}
which is shorter than the proper length. Hence, the same rod can have different lengths in different inertial frames .

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