Question

A person standing on a platform finds that a train moving with velocity 0.6c takes one second to pass by him. Find (a) the length of the train as seen by the person and (b) the rest length of the train.

Answer 1

Given:
Velocity of train, v = 0.6c
Time taken, t = 1 s

(a) Length observed by the observer, L= vt
⇒ L = 0.6 × 3 × 10⁸
= 1.8 × 10⁸ m

(b) Let the rest length of train be L₀. Then,
$L=L_0\sqrt{1-v^2/c^2}$
$$\begin{gathered} \Rightarrow 1.8\times {10}^8=L_0\sqrt{1-\frac{{\left(0.6\right)}^2{c}^2}{c^2}} \\ \Rightarrow 1.8\times {10}^8=L_0\times 0.8 \\ \Rightarrow L_0=\frac{1.8\times {10}^8}{0.8} \\ \Rightarrow L_0=2.25\times {10}^8\mathrm{m} \end{gathered}$$