Question

The density of a stationary body is equal to ρ_o. Find the velocity (relative to the body) of the reference frame in which the density of the body is η = 25% greater than ρ_o.

Answer 1

We define the density ρ in the frame K in such a way that ρdx dy dz is the rest mass dm_o of the element That is ρdx dy dz = ρ_odx_o dy_o dz_o , where ρ_o is the proper density dx_o, dy_o, dz_o are the dimensions of the element in the rest frame K_o . Now

if the frame K is moving with velocity, v relative to the frame K₀ . Thus