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 .

Explanation

Given ` v = 0.6 cm / sec , t = 1 sec`
(a) Length observed by the observer
` = vt = 0.6 xx 3 xx 10^(6) `
` = 1.8 xx 10^(6) m
(b) `L = L_0 (sqrt 1 - v^(2) / c^(2) ) `
` rArr 1.8 xx 10^(8) = L_0 (sqrt (1-) (0.6)^(2) c^(2) / c^(2) `
` rArr 1. 8xx 10^(8) = L_0 xx 0.8`
` rArr L_0 = 1.8 xx 10^(8) / 0.8 `
` 2.25 xx 10^(3) m /s `