CBSE-XI-Physics
47: The Special Theory of Relativity
- #20By what fraction does the mass of a boy increase when he starts running at a speed of 12 km h-1?Ans : Given: Speed of the boy, v = 12 km h-1 = 10/3 m/s
Let the rest mass of the boy be m.
Kinetic energy of the boy, `` E=\frac{1}{2}m{v}^{2}``
`` \Rightarrow E=\frac{1}{2}m{\left(\frac{10}{3}\right)}^{2}=\frac{m\times 50}{9}``
`` ``
Increase in energy of the body = Kinetic energy of the boy
This increase in energy is converted into mass. Thus,
`` \,\mathrm{\,Increase\,}\,\mathrm{\,in\,}\,\mathrm{\,mass\,}=∆m=\frac{E}{{c}^{2}}``
`` ∆m=\frac{m\times 50}{9\times 9\times {10}^{16}}``
`` \,\mathrm{\,Fraction\,}\,\mathrm{\,increase\,}\,\mathrm{\,in\,}\,\mathrm{\,mass\,}=\frac{∆m}{m}=\frac{50}{81\times {10}^{16}}``
`` \Rightarrow \frac{∆m}{m}=\frac{50}{81}\times {10}^{-16}=6.17\times {10}^{-17}``
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