CBSE-XI-Physics
47: The Special Theory of Relativity
- #16-ain the lab frame and (b) in the frame of the particle.Ans : Life of the particle in the lab frame is given by
`` t=\frac{d}{v}=\frac{0.01}{0.995c}``
`` =\frac{0.01}{0.995\times 3\times {10}^{8}}``
`` =33.5\times {10}^{-12}\,\mathrm{\,s\,}=33.5\,\mathrm{\,ps\,}`` (b) Let the life of the particle in the frame of the particle be t'. Thus,
`` t\text{'}=\frac{t}{\sqrt{1-{v}^{2}/{c}^{2}}}``
`` t\text{'}=\frac{33.5\times {10}^{-12}}{\sqrt{1-{\left(0.995\right)}^{2}}}``
`` t\text{'}=3.3541\times {10}^{-12}\,\mathrm{\,s\,}=3.3541\,\mathrm{\,ps\,}``
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- #16-bin the frame of the particle.Ans : Let the life of the particle in the frame of the particle be t'. Thus,
`` t\text{'}=\frac{t}{\sqrt{1-{v}^{2}/{c}^{2}}}``
`` t\text{'}=\frac{33.5\times {10}^{-12}}{\sqrt{1-{\left(0.995\right)}^{2}}}``
`` t\text{'}=3.3541\times {10}^{-12}\,\mathrm{\,s\,}=3.3541\,\mathrm{\,ps\,}``
Page No 458: