All Problems Relativistic Mechanics
Problem 1.369
The density of a stationary body is equal to \(\rho_{0}\). Find the velocity (relative to the body) of the reference frame in which the density of the body is \(\eta=25 \%\) greater than \(\rho_{0}\).
1.369. \(v=c \sqrt{\eta(2+\eta) /(1+\eta)}=0.6 c,\) where \(c\) 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.