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Two rods having the same proper length l_0 move lengthwise toward each other parallel to a common axis with the same velocity v relative to the laboratory frame of reference. What is the length of each rod in the reference frame fixed to the other rod? |
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Answer» Solution :The VELOCITY of one of the rods in the reference FRAME FIXED to the other ROD is `V=(v+v)/(1+v^2/c^2)=(2V)/(1+beta^2)` The length of the moving rod in this frame is `l=l_0sqrt(1-(4v^2//c^2)/((1+beta^2)^2))=l_0(1-beta^2)/(1+beta^2)` |
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