The length of a moving meter stick is 75 cm.What is its speed parallel to its length?
A)0.25 c
B)0.50 c
C)0.66 c
D)0.78 c

Question

Quizplus · Accepted Answer

The length contraction formula is $L = L_0\sqrt{1 - \frac{v^2}{c^2}}$, where $L$ is the observed length, $L_0$ is the proper length (the length of the object in its rest frame), and $v$ is the velocity of the object. Rearranging the formula to solve for $v$, we get $v = c\sqrt{1 - \frac{L^2}{L_0^2}}$. Substituting $L = 75$ cm and $L_0 = 100$ cm (since a meter stick's proper length is 100 cm), we find $v = c\sqrt{1 - (0.75)^2} = c\sqrt{1 - 0.5625} = c\sqrt{0.4375} \approx 0.66c$.

The Length of a Moving Meter Stick Is 75 Cm