CBSE-XI-Physics
47: The Special Theory of Relativity
- #17By 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-1.Ans : Given:
Compression in the string, x = 1 cm = 1 × 10-2 m
Spring constant, k = 500 N/m
Mass of the spring, m = 200 g = 0.2 kg
Energy stored in the spring, E`` =\frac{1}{2}k{x}^{2}``
`` \Rightarrow E=\frac{1}{2}\times 500\times {10}^{-4}``
`` =0.025\,\mathrm{\,J\,}``
This energy can be converted into mass according to mass energy equivalence. Thus,
`` \,\mathrm{\,Increase\,}\,\mathrm{\,in\,}\,\mathrm{\,mass\,},∆m=\frac{E}{{c}^{2}}``
`` =\frac{0.025}{{c}^{2}}``
`` =\frac{0.025}{9\times {10}^{16}}\,\mathrm{\,kg\,}``
`` \,\mathrm{\,Fractional\,}\,\mathrm{\,change\,}\,\mathrm{\,of\,}\,\mathrm{\,mass\,},\frac{∆m}{m}=\frac{0.025}{9\times {10}^{16}}\times \frac{1}{0.2}``
`` \Rightarrow \frac{∆m}{m}=0.01388\times {10}^{-16}``
`` \Rightarrow \frac{∆m}{m}=1.4\times {10}^{-18}``
`` ``
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