Question

A rod of rest length L moves at a relativistic speed. Let L' = L/γ. Its length

(a) must be equal to L'
(b) may be equal to L
(c) may be more than L' but less than L
(d) may be more than L

Answer 1

(b) may be equal to L
(c) may be more than L' but less than L

If a rod of rest length L is moving at a relativistic speed v and its length is contracted to L', then

$$\begin{gathered} L\text{'}=\frac{L}{\gamma }=L\sqrt{1-\frac{v^2}{c^2}} \\ \mathrm{If}\gamma =\frac{1}{\sqrt{1-{\displaystyle \frac{v^2}{c^2}}}},\mathrm{then}v<<c,\gamma \cong 1. \\ \Rightarrow L\text{'}\cong L \end{gathered}$$

But the length of the rod may be more than L' depending on the frame of the observer. However, it cannot be more than L because as the speed of the rod increases, its length contracts more and more due to increasing value of $\gamma$.