Two independent events occur 100 m apart with an intervening time interval of 0.42 $\mu$s.The proper time between the events is:
A)0 $\mu$s
B)0.16$\mu$s
C)0.26 $\mu$s
D)0.42 $\mu$s
E)0.69$\mu$s

Question

Quizplus · Accepted Answer

The proper time between two events is given by the formula Δτ = Δt/γ, where Δt is the time interval between the events in some reference frame and γ is the Lorentz factor. In this case, the time interval between the events is Δt = 0.42 μs. The Lorentz factor depends on the relative velocity of the reference frame in which the events are observed. However, since the events are 100 m apart, it is reasonable to assume that the relative velocity is much smaller than the speed of light and we can use the approximation γ ≈ 1. Therefore, the proper time between the events is Δτ = Δt/γ ≈ 0.42 μs. The only answer that matches this value is C.

Two Independent Events Occur 100 M Apart with an Intervening μ\muμ

Two Independent Events Occur 100 M Apart with an Intervening $\mu$