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Q8PE

Expert-verifiedFound in: Page 1029

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**If relativistic effects are to be less than 3%, then γ must be less than 1.03. At what relative velocity is γ = 1.03?**

The relative velocity v* = *0.240*c.*

As we know the relativistic factor is given by

\(\gamma=\frac{1}{{\sqrt{1-{{\left({\frac{v}{c}}\right)}^2}}}}\) …. (1)

Where v is its velocity relative to an observer and *c *= 3.00 ×10^{8 }m/s is the speed of the light

Here given that the relativistic factor is

γ = 1.03

From the equation (1), we get

\(\begin{aligned}v &=c\sqrt{1-{{\left({\frac{1}{\gamma}}\right)}^2}}\\&=c\sqrt{1-{{\left({\frac{1}{{1.03}}} \right)}^2}} \\&= 0.240c\end{aligned}\)

Hence the relative velocity is *v = *0.240*c*

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