Question

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?

Short answer

The relative velocity v=0.240c.

Step-by-step solution

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 ×10⁸m/s is the speed of the light

Here given that the relativistic factor is

γ = 1.03

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