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Question

Two rods having the same proper length l0 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 other rod in the reference frame fixed to the other rod?
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Solution

The velocity of one of the rods in the reference frame fixed to the other rod is
V=ν+ν1+ν2c2=2ν1+β2
The length of the moving rod in this frame is
l=l014ν2/c2(1+β2)2=l01β21+β2

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