A suitcase kept on a shop's rack is measured` 50 cm xx 25 cm xx 10 cm by the shop's owner . A traveller takes this suitcase in a train moving with velocity 0.6c . If the suitcase is placed with its length along the trains velocity , find the dimensions mesured by (a) the traveller and (b)a ground observe .

Explanation

Given `l = 50cm , b = 2.5 cm `
`h = 10cm , v = 0.06c `
(a) The observe in the train the same value of l , b, h because realtivity is due to the difference in frames .
(b) In two different frames , the component of length parallel to the velocity undergoes contraction but the p components remain the same . So length which is parallel to the x- axis changes and the breadth and height ramain the same .
` e' = e (sqrt 1 - v^(2) / c^(2) ) `
` = 50 (sqrt 1 - (0.6)^(2) c^(2) / c^(2)) `
` l = 50 (sqrt 1 -0.326 ) `
` =50 (sqrt 0.64) `
` = 50 xx 0.8 = 40 cm`.
` .:` The lenghts observed are 40cm xx 25 cm xx 10cm`