NEET-XII-Physics
47: The Special Theory of Relativity
- #12If a person lives on the average 100 years in his rest frame, how long does he live in the earth frame if he spends all his life on a spaceship going at 60% of the speed of light.Ans : Given:
Proper time, t = 100 years
Speed of spaceship, v = `` \frac{60}{100}c`` = 0.60c
`` ∆t\text{'}=\frac{∆t}{\sqrt{1-{\displaystyle \frac{{v}^{2}}{{c}^{2}}}}}``
`` =\frac{100}{\sqrt{1-{\left(0.60\right)}^{2}{\displaystyle \frac{{c}^{2}}{{c}^{2}}}}}``
`` =\frac{100}{0.8}=125\,\mathrm{\,y\,}``
Thus, the person lives for 125 years in the Earth frame.
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