A meter stick moves in the direction of its length through a laboratory.According to measurements taken in the laboratory, its length is 0.31 m.The speed of the meter stick relative to the laboratory is:
A)0.096c
B)0.31c
C)0.69c
D)0.83c
E)0.95c

Question

Quizplus · Accepted Answer

The length contraction formula in special relativity is given by $L = L_0\sqrt{1 - \frac{v^2}{c^2}}$, where $L$ is the contracted length, $L_0$ is the rest length, $v$ is the relative velocity, and $c$ is the speed of light. Rearranging for $v$, we get $v = c\sqrt{1 - \frac{L^2}{L_0^2}}$. Substituting $L = 0.31$ m (contracted length) and $L_0 = 1$ m (rest length of the meter stick), we find $v \approx 0.95c$, indicating the meter stick is moving at 95% the speed of light relative to the laboratory.

A Meter Stick Moves in the Direction of Its Length