Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Suppose Swarglok (Heaven) is in Constant Motion at a Speed of 0.9999c with Respect to the Earth. According to the Earth'S Frame, How Much Time Passes on the Earth before One Day Passes on Swarglok? - Physics

Sum

Suppose Swarglok (heaven) is in constant motion at a speed of 0.9999c with respect to the earth. According to the earth's frame, how much time passes on the earth before one day passes on Swarglok?

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Solution

Given:-
Speed of Swarglok, v = 0.9999c
Proper time interval, ∆t = One day on Swarglok

Suppose ∆t' days pass on Earth before one day passes on Swarglok.
Now,

\[∆ t' = \frac{∆ t}{\sqrt{1 - \frac{v^2}{c^2}}}\]
\[ = \frac{1}{\sqrt{1 - \frac{\left( 0 . 9999 \right)^2 c^2}{c^2}}}\]
\[ = \frac{1}{0 . 014141782} = 70 . 712\text{ days}\]

Thus,

∆t' = 70.7 days

Concept: Twin Paradox
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 25 The Special Theory of Relativity
Q 11 | Page 458
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