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The Special Theory of Relativity — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsThe Special Theory of Relativity3 Marks
Question
A person standing on a platform finds that a train moving with velocity $0.6c$ takes one second to pass by him. Find:
  1. The length of the train as seen by the person and.
  2. The rest length of the train.
✓

Answer

$\text{v}=0.6\text{cm/sec};\text{t}=1\sec$
  1. Length observed by the observer $= vt$
$\Rightarrow0.6\times3\times10^{6}$
$\Rightarrow1.8\times10^{8}\text{m}$
  1. $\ell=\ell_0\sqrt{1-\frac{\text{v}^2}{\text{c}^2}}\Rightarrow1.8\times10^{8}$
$=\ell_0\sqrt{1-\frac{(0.6)^2\text{c}^2}{\text{C}^2}}$
$\ell_0=\frac{1.8\times10^{8}}{0.8}$
$=2.25\times10^{8}\text{m}/\text{s}.$

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