Question

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

Answer 1

From the formula for length contraction
`(l_0-l_0sqrt(1-v^2/c^2))=etal_0`
So, `1-v^2/c^2=(1-eta)^2` or `v=csqrt(eta(2-eta))`