Q7PE - College Physics (Urone)

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?

 

Step-by-Step Solution

Answer

The relative velocity is v = 0.140c.

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 = 1.01

Step 2: To solve the equation

From the equation (1 ), we get 

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

Hence the relative velocity is v = 0.140c.