An object of rest length $L_{R}$ moving at one-half the speed of light will have a length equal to:
A) $\frac{1}{2} L_{R}$
B) $\frac{3}{4} L_{R}$
C) $\left(\frac{1}{2}\right)^{1 / 2} L_{R}$
D) $0.87 L_{R}$
E) $\frac{1}{4} L_{R}$
F) Other (specify)

Question

Quizplus · Accepted Answer

The length contraction formula in special relativity is $L = L_{R} \sqrt{1 - v^2/c^2}$, where $L$ is the observed length, $L_{R}$ is the rest length, $v$ is the velocity of the object, and $c$ is the speed of light. Substituting $v = 0.5c$, we get $L = L_{R} \sqrt{1 - (0.5)^2} = L_{R} \sqrt{0.75} = 0.866 L_{R}$, which rounds to $0.87 L_{R}$.  $L=\sqrt{1-\beta^{2}} L_{R}=\sqrt{1-0.25} L_{R}=0.866 L_{R}$.

An Object of Rest Length LRL_{R}LR​ Moving at One-Half the Speed of Light Will Have a Speed

An Object of Rest Length $L_{R}$ Moving at One-Half the Speed of Light Will Have a Speed