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Relativistic Mechanics

Problem 1.369

The density of a stationary body is equal to ρ0\rho_{0}. Find the velocity (relative to the body) of the reference frame in which the density of the body is η=25%\eta=25 \% greater than ρ0\rho_{0}.

Reveal Answer
1.369. v=cη(2+η)/(1+η)=0.6c,v=c \sqrt{\eta(2+\eta) /(1+\eta)}=0.6 c, where cc is the velocity of light. The definition of density as the ratio of the rest mass of a body to its volume is employed here.
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