Verified Solution • 2025–26 Session moderate

QPage 458: Q4: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Page 458: Q4 Solution: A person standing on a platform finds that a train moving with…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently invert the length contraction formula, calculating the rest length as $L_0 = L\sqrt{1 - v^2/c^2}$, which incorrectly implies the moving object is longer than its rest length. Remember that the observed length $L$ is always shorter than the rest length $L_0$, so you must divide by the Lorentz factor (or multiply by $1/\gamma$) to find $L_0$.

A person standing on a platform finds that a train moving with velocity 0.6c takes one second to pass by him. Find a) the length of the train as seen by the person and b) the rest length of the train.

Step-by-Step Verified Solution

**Answer:** (a) Length of train = 1.8×1081.8 \times 10^8 m (b) Rest length = 2.25×1082.25 \times 10^8 m. **Step-by-Step Explanation:** (a) The person on the platform measures the moving train. Time to pass = 1 s, speed = 0.6c=1.8×1080.6c = 1.8 \times 10^8 m/s. Contracted length L=v×t=1.8×108×1=1.8×108L = v \times t = 1.8 \times 10^8 \times 1 = 1.8 \times 10^8 m. (b) L=L01−v2/c2=L01−0.36=0.8L0L = L_0\sqrt{1 - v^2/c^2} = L_0\sqrt{1 - 0.36} = 0.8L_0. L0=L/0.8=1.8×108/0.8=2.25×108L_0 = L/0.8 = 1.8 \times 10^8 / 0.8 = 2.25 \times 10^8 m.

All Questions in this Chapter

QPage 457: Q1 QPage 457: Q2 QPage 457: Q3 QPage 457: Q4 QPage 457: Q5 QPage 457: Q6 QPage 457: Q7 QPage 457: Q8 QPage 457: Q9 QPage 457: Q10 QPage 457: Q11 QPage 457: Q12 QPage 457: Q13 QPage 458: Q1 QPage 458: Q2 QPage 458: Q3 QPage 458: Q4 QPage 458: Q5 QPage 458: Q6 QPage 458: Q7 QPage 458: Q8 QPage 458: Q9 QPage 458: Q10 QPage 458: Q11 QPage 458: Q12 QPage 458: Q13 QPage 458: Q14 QPage 458: Q15 QPage 458: Q16 QPage 458: Q17 QPage 458: Q18 QPage 458: Q19 QPage 458: Q20 QPage 458: Q21 QPage 458: Q22 QPage 458: Q23 QPage 458: Q24 QPage 458: Q25 QPage 458: Q26 QPage 458: Q27 QPage 458: Q28 QPages 456-457: Q1 QPages 456-457: Q2 QPages 456-457: Q3 QPages 456-457: Q4 QPages 456-457: Q5

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from The Special Theory of Relativity
Reference Textbook Solutions
Explore complete chapter exercises for HC Verma: Concepts of Physics - Volume 2
Competitive PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring