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College Physics (Urone)
Found in: Page 1029

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Short Answer

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 = 0.240c.

See the step by step solution

Step by Step Solution

Step 1: To find the relative velocity

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 ×108 m/s is the speed of the light

Here given that the relativistic factor is

γ = 1.03

Step 2: To solve the equation

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 = 0.240c

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