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Relativistic Mechanics

Problem 1.345

A rod flies with constant velocity past a mark which is stationary in the reference frame \(K .\) In the frame \(K\) it takes \(\Delta t=\) \(=20\) ns for the rod to fly past the mark. In the reference frame fixed to the rod the mark moves past the rod for \(\Delta t^{\prime}=25 \mathrm{~ns}\). Find the proper length of the rod.

Reveal Answer
l0=cΔt′1−(Δt/Δt′)2=4.5 ml_{0}=c \Delta t^{\prime} \sqrt{1-\left(\Delta t / \Delta t^{\prime}\right)^{2}}=4.5 \mathrm{~m}
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