Answer
The length measured by an observer on the Earth is less than 1.00 m, as long as some component of the rod's orientation is parallel to the direction of motion.
If the rod is oriented perpendicular to the direction of motion, the length measured by an observer on the Earth is equal to 1.00 m
Therefore, the answer depends on the orientation of the rod.
Work Step by Step
Let $L_0 = 1.00~m$. We can find the length measured by the observer if the rod is oriented parallel to the direction of motion:
$L = L_0~\sqrt{1-\frac{v^2}{c^2}} \lt L_0$
The length measured by an observer on the Earth is less than 1.00 m, as long as some component of the rod's orientation is parallel to the direction of motion.
If the rod is oriented perpendicular to the direction of motion, the length measured by an observer on the Earth is equal to 1.00 m
Therefore, the answer depends on the orientation of the rod.
