Special Relativity - Relativistic Momentum

If the total energy of a particle of mass m is equal to twice its rest energy, then the magnitude of the particle’s relativistic momentum is

A. mc/2
B. mc/√2
C. mc
D. √3mc
E. 2mc

(GR0177 #32)

Solution:

Rest Energy: E₀ = m₀c²

Relativistic Energy:  E² = p²c² + m₀²c⁴

Given: m₀ = m and E = 2E₀

p²c² + m²c⁴ = 4E₀² = 4m²c⁴
p² = 3m²c²
p = √3mc

Answer: D