You place two clocks that you consider to be synchronized on a road 100 m apart.Your friend drives by at speed V and observes the clocks to be out of sync by an amount T.When you place the clocks 200 m apart and your friend drives by at speed 2V,by what amount will your friend claim the clocks to be out of sync?
A)T
B)2T
C)4T
D)T/2
E)T/4

Question

Quizplus · Accepted Answer

The time dilation formula is:$$T' = \frac{T}{\gamma}$$where:* $T'$ is the time interval measured in the moving frame* $T$ is the time interval measured in the stationary frame* $\gamma$ is the Lorentz factor, which is given by:$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$where:* $v$ is the speed of the moving object* $c$ is the speed of lightIn this problem, we are given that the clocks are 100 m apart and that your friend drives by at speed $V$. We are also told that your friend observes the clocks to be out of sync by an amount $T$. This means that:$$T' = T - \frac{100 m}{V}$$We are then asked to find the amount of time by which your friend will claim the clocks to be out of sync when the clocks are 200 m apart and your friend drives by at speed $2V$. This means that:$$T'' = T - \frac{200 m}{2V}$$Substituting the first equation into the second equation, we get:$$T'' = T - \frac{100 m}{V} - \frac{100 m}{2V}$$$$T'' = T - \frac{200 m}{2V}$$$$T'' = T - \frac{100 m}{V}$$Therefore, the amount of time by which your friend will claim the clocks to be out of sync when the clocks are 200 m apart and your friend drives by at speed $2V$ is $T$.

You Place Two Clocks That You Consider to Be Synchronized