Length contraction: Relative to the frame of the observer making the measurement, at what speed parallel to its length is the length of a meterstick 60 cm?
A) 0.80c
B) 0.60c
C) 0.50c
D) 0.70c
E) 0.90c

Question

Quizplus · Accepted Answer

Length contraction is given by the formula $L = L_0\sqrt{1 - v^2/c^2}$, where $L$ is the contracted length, $L_0$ is the rest length, $v$ is the velocity, and $c$ is the speed of light. Given $L = 60$ cm and $L_0 = 100$ cm (since a meter stick's rest length is 100 cm), we solve for $v$ to find the speed that results in a 60 cm observed length. Plugging the values into the formula and solving for $v$, we find that $v = 0.80c$, indicating that the meterstick must be moving at 80% the speed of light relative to the observer for its length to contract to 60 cm.

Length Contraction: Relative to the Frame of the Observer Making