Question

Find the velocity at which the relativistic momentum of a particle exceeds its Newtonian momentum `eta=2` times.

Answer 1

By definition of `eta`,
`(m_0v)/(sqrt(1-v^2/c^2))=etam_0v` or `1-v^2/c^2=1/eta`
or `v=csqrt(1-(1)/(eta^2))=c/etasqrt(eta^2-1)`