Answer
$L'=0.0644mm$
Work Step by Step
Relativistic time is defined as $$\Delta t=\gamma \Delta t_p$$ Substituting a known value of $v=0.960c$ and $\beta=0.960$ into the gamma expression yields a gamma value of $$\gamma=\frac{1}{\sqrt{1-0.960^2}}=3.57$$ Using the formula $$L'=\frac{L}{\gamma}$$ and the known values of $L=0.230mm$ and $\gamma=3.57$ yields an L' value of $$L'=\frac{0.230mm}{3.57}=0.0644mm$$
