Final answer:
The correct relative velocity where the relativistic factor γ equals 2.00 is (a) 0.866c, which is derived from solving the equation γ = (1 − (v2/c2))−1/2 with γ set to 2. Therefore, the correct option is (a) 0.866c.
Step-by-step explanation:
The student is asking about the relativistic factor γ (gamma), which is defined in special relativity to describe the factor by which time, length, and relativistic mass change for an object while that object is moving. The equation for gamma is γ = (1 − (v2/c2))−1/2, where v is the velocity of the object and c is the speed of light.
To find out at what relative velocity γ is 2.00, we would solve for v where γ = 2. The equation becomes 2 = (1 − (v2/c2))−1/2, which simplifies to v = c ∙ √(1 - (1/4)). This gives us v = 0.866c when rounded to three decimal places. Therefore, the correct option is (a) 0.866c.