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A suitcase kept on a shop's rack is measured 50 cm xx 25 cm xx 10 cm xx 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 . |
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Answer» Solution :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 remainthe 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` |
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