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

Explanation:

It is given:

Train has the velocity, v = 0.6c

Time taken, t = 1 s

(a) The observer observes the length, L = vt

$L=3 \times 0.6 \times 10^{8}$

$=1.8 \times 10^{2} \mathrm{m}$

(b) The length of the train is indicated with the rest length of train indicated as $L_O$. Then, $\mathrm{L}=\mathrm{LO} 1-\mathrm{v} 2 / \mathrm{c} 2$

$\Rightarrow 1.8 \times 108=\angle 0 \times 0.8$

$\Rightarrow \mathrm{LO}=1.8 \times 1080.8$

$\Rightarrow \mathrm{LO}=2.25 \times 108 \mathrm{m}$