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?

(a) 0.0297c
(b) 0.0300c
(c) 0.0303c
(d) 0.0306c

Answer 1

To find the relative velocity at which γ = 1.03, we can rearrange the equation γ = 1/√(1 - v^2/c^2) and solve for v. Plugging in γ = 1.03 gives v ≈ 0.0300c.

Step-by-step explanation:

In relativistic physics, the Lorentz factor (γ) is given by γ = 1/√(1 - v^2/c^2), where v is the relative velocity and c is the speed of light.

The question states that γ must be less than 1.03 to ensure relativistic effects are less than 3%.

To find the relative velocity, we can rearrange the equation to solve for v.

Plugging in γ = 1.03, we get v = √(1 - 1/1.03^2) * c. Evaluating this expression gives approximately 0.0300c, so the answer is (b) 0.0300c.