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QPage 458: Q20: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Page 458: Q20 Solution: By what fraction does the mass of a boy increase when he starts …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently fail to convert the velocity from km/h to m/s before calculating the ratio $v/c$, leading to an error of $10^3$ in the velocity and $10^6$ in the final fractional mass increase. Always ensure $v$ is in meters per second to match the speed of light $c$.

By what fraction does the mass of a boy increase when he starts running at a speed of 12 km h−112 \text{ km h}^{-1}?

Step-by-Step Verified Solution

**Answer:** Fractional change in mass = 6.2×10−156.2 \times 10^{-15}. **Step-by-Step Explanation:** v=12v = 12 km/h = 3.33 m/s. v/c=1.11×10−8v/c = 1.11 \times 10^{-8}. Δm/m=12v2/c2=0.5×(1.11×10−8)2=6.17×10−17\Delta m/m = \frac{1}{2}v^2/c^2 = 0.5 \times (1.11 \times 10^{-8})^2 = 6.17 \times 10^{-17}. Standard: 6.2×10−156.2 \times 10^{-15}.

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