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Relativistic Mechanics

Problem 1.340

1.340.1.340 . A rod moves lengthwise with a constant velocity vv relative to the inertial reference frame K.K . At what value of vv will the length of the rod in this frame be η=0.5%\eta=0.5 \% less than its proper length?

Reveal Answer
1.340. v=cη(2η)=0.1c,v=c \sqrt{\eta(2-\eta)}=0.1 c, where cc is the velocity of light.