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Question: Answered & Verified by Expert
An observer 'A' sees an asteroid with a radioactive element moving by at a speed $=0.3 \mathrm{c}$ and measures the radioactivity decay time to be $\mathrm{T}_{\mathrm{A}^{\prime}}$. Another observer ' $\mathrm{B}$ ' is moving with the asteroid and measures its decay time as $\mathrm{T}_{\mathrm{B}}$. Then $\mathrm{T}_{\mathrm{A}}$ and $\mathrm{T}_{\mathrm{B}}$ are related as below
PhysicsElectromagnetic WavesVITEEEVITEEE 2008
Options:
  • A $\mathrm{T}_{\mathrm{B}} < \mathrm{T}_{\mathrm{A}}$
  • B $\mathrm{T}_{\mathrm{A}}=\mathrm{T}_{\mathrm{B}}$
  • C $\mathrm{T}_{\mathrm{B}}>\mathrm{T}_{\mathrm{A}}$
  • D Either (A) or (C) depending on whether the asteroid is approaching or moving away from A
Solution:
1190 Upvotes Verified Answer
The correct answer is: $\mathrm{T}_{\mathrm{B}}>\mathrm{T}_{\mathrm{A}}$
Due to time dilation the interval between two events at the same point in a moving frame appears to be longer by a factor
$\gamma\left(\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\right)$ to an observer in a stationary frame.
Time dilation is independent of the direction of velocity and depends only on its magnitude.

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