Reference frames — UPSC Physics Optional CSE 2019 Paper I

(i) A reference frame S' moves with respect to rest frame S with a uniform velocity v parallel to x-direction. Show from Lorentz transformation that two events simultaneous (t_1=t_2) at different positions (x_1\ne x_2) in S frame are not in general simultaneous in S' frame.

(ii) The mean life of \pi meson is 2\times10^{-8}\,\mathrm{s}. Calculate the mean life of a meson moving with a velocity of 0.8c, where c is the velocity of light.