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?

a) 0.995c
b) 0.998c
c) 0.999c
d) 1.002c

Answer 1

The relative velocity at which γ = 1.01 is 0.99995c.

Step-by-step explanation:

In order for relativistic effects to be less than 1%, the value of γ must be less than 1.01. The equation for γ is γ = 1 / sqrt(1 - (v^2 / c^2)), where v is the velocity and c is the speed of light. To find the relative velocity when γ = 1.01, we can rearrange the equation to solve for v. Plugging in γ = 1.01, we get v = c * sqrt(1 - (1 / γ^2)). Calculating this value, we find that v = 0.99995c, which corresponds to option (b) 0.99995c.