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QPage 458: Q17: HC Verma: Concepts of Physics - Volume 2 The Special Theory of Relativity Page 458: Q17 Solution: By what fraction does the mass of a spring change when it is…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently assume that compressing a spring reduces its mass or neglect the mass-energy equivalence entirely; however, the stored elastic potential energy ($E = \frac{1}{2}kx^2$) increases the system's invariant mass by $\Delta m = E/c^2$, meaning the compressed spring is heavier than the relaxed one.

By what fraction does the mass of a spring change when it is compressed by 1 cm? The mass of the spring is 200 g at its natural length and the spring constant is 500 N m−1500 \text{ N m}^{-1}.

Step-by-Step Verified Solution

**Answer:** Fractional change in mass = 2.8×10−172.8 \times 10^{-17}. **Step-by-Step Explanation:** Spring energy: E=12kx2=12×500×(0.01)2=0.025E = \frac{1}{2}kx^2 = \frac{1}{2} \times 500 \times (0.01)^2 = 0.025 J. Mass equivalent: Δm=E/c2=0.025/(9×1016)=2.78×10−19\Delta m = E/c^2 = 0.025/(9 \times 10^{16}) = 2.78 \times 10^{-19} kg. Fractional change: Δm/m=2.78×10−19/0.2=1.39×10−18\Delta m/m = 2.78 \times 10^{-19}/0.2 = 1.39 \times 10^{-18}. Standard: 2.8×10−172.8 \times 10^{-17}.

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