NEET-XII-Physics
47: The Special Theory of Relativity
- #8A person travels on a spaceship moving at a speed of 5c/13. (a) Find the time interval calculated by him between the consecutive birthday celebrations of his friend on the earth. (b) Find the time interval calculated by the friend on the earth between the consecutive birthday celebrations of the traveller.Ans : Given: Speed of spaceship, `` u=\frac{5c}{13}`` (a) Proper time, t = 1 yr
`` \,\mathrm{\,Time\,}intervalcalculatedbyhim=t\text{'}=\frac{t}{\sqrt{1-{u}^{2}/{c}^{2}}}``
`` =\frac{1\,\mathrm{\,yr\,}}{\sqrt{1-{\displaystyle \frac{25{c}^{2}}{169{c}^{2}}}}}``
`` =\frac{13}{12}\,\mathrm{\,yr\,}``
`` ``
Thus, the time interval calculated by him between the consecutive birthday celebrations of his friend on Earth is 13/12 years. (b) The friend on Earth also considers the same speed, so the time interval calculated by him is also 13/12 years.
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- #8-aFind the time interval calculated by him between the consecutive birthday celebrations of his friend on the earth.Ans : Proper time, t = 1 yr
`` \,\mathrm{\,Time\,}intervalcalculatedbyhim=t\text{'}=\frac{t}{\sqrt{1-{u}^{2}/{c}^{2}}}``
`` =\frac{1\,\mathrm{\,yr\,}}{\sqrt{1-{\displaystyle \frac{25{c}^{2}}{169{c}^{2}}}}}``
`` =\frac{13}{12}\,\mathrm{\,yr\,}``
`` ``
Thus, the time interval calculated by him between the consecutive birthday celebrations of his friend on Earth is 13/12 years.
- #8-bFind the time interval calculated by the friend on the earth between the consecutive birthday celebrations of the traveller.Ans : The friend on Earth also considers the same speed, so the time interval calculated by him is also 13/12 years.
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