The length of a meter stick moving at 0.95c in the direction of its length is measured by simultaneously marking its ends on a stationary axis. As measured by clocks moving with the stick, the time interval between the making of the back mark and the making of the front mark is: A) 0 B) 3.1 * 10^-¹⁰ s C) 1.0 * 10^-⁹ s D) 3.2 *10^-⁹ s E) 1.0 *10^-⁸ s

Question

Quizplus · Accepted Answer

According to the formula for time dilation:
Δt' = Δt/√(1-v^2/c^2)
where Δt is the time interval measured in the rest frame of the meter stick (stationary axis) and v is the velocity of the meter stick in that frame.
In this case, v = 0.95c and Δt is the time interval between the markings on the meter stick. Therefore:
Δt' = Δt/√(1-0.95^2)
Δt' = Δt/√(1-0.9025)
Δt' = Δt/0.4369
Δt' = 2.289Δt
This means that as measured by clocks moving with the meter stick, the time interval is dilated by a factor of 2.289. Therefore, the time interval between the markings is:
Δt' = 19 s / 2.289
Δt' = 8.299 s
This is closest to choice D, 3.2 x 10^-9 s.

The Length of a Meter Stick Moving at 0