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

\[L' = \frac{L}{\gamma} = L\sqrt{1 - \frac{v^2}{c^2}}\]

If \[\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}},\text{ then }v <  < c,   \gamma \cong 1 . \]

\[ \Rightarrow L' \cong L\]

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.`