[UPSC CSE 2001] Special Theory of Relativity (Q394, 20M)

The mass of muon at rest is 207\text{ m}_e where m_e is the electron rest mass (0.511\text{ MeV}). The mean life time at rest for muon is 2.2\ \mu\text{s}. The life time of muon emerging from an accelerator is measured in the laboratory as 6.9\ \mu\text{s}. Estimate the speed of these muons in the laboratory.