Q8PE - College Physics (Urone)

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?

Step-by-Step Solution

Answer

The relative velocity v = 0.240c.

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