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QPage 458: Q12: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Page 458: Q12 Solution: If a person lives on the average 100 years in his rest frame,…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently confuse the proper time ($\Delta t_0$) with the dilated time ($\Delta t$), leading them to divide by the Lorentz factor instead of multiplying. Remember that the lifetime measured in the person's rest frame is the proper time, so the Earth observer must calculate $\Delta t = \gamma \Delta t_0$ to find the longer duration.

If a person lives on the average 100 years in his rest frame, how long does he live in the earth frame if he spends all his life on a spaceship going at 60% of the speed of light.

Step-by-Step Verified Solution

**Answer:** 125 years. **Step-by-Step Explanation:** v=0.6cv = 0.6c. γ=1/1−0.36=1/0.8=1.25\gamma = 1/\sqrt{1 - 0.36} = 1/0.8 = 1.25. Δt=γΔt0=1.25×100=125\Delta t = \gamma \Delta t_0 = 1.25 \times 100 = 125 years.

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