Question

If relativistic effects are to be less than 1%, then γ must be less than 1.01. At what relative velocity is γ = 1.01?

Short answer

The relative velocity is v =0.140c.

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 = 1.01

To solve the equation

From the equation (1 ), we get

\(\begin{aligned} v &= c\sqrt {1-{{\left( {\frac{1}{\gamma }}\right)}^2}} \\&= c\sqrt {1-{{\left( {\frac{1}{{1.01}}} \right)}^2}} \\&= 0.140c \end{aligned}\)

Hence the relative velocity is v =0.140c.