How do the measured densities of a body compare at rest and in motion?
Solution 29E Step 1 of 3 : Density is the ratio of mass by volume or mass per unit volume. That is = m V Where is the density, m is the mass and V is volume. Under relativistic case, In rest frame the mass and volume will be different than the mass and volume when the frame is moving. The density at rest, mo o Vo Where is the density at rest,m isothe rest mass and V o is the volume in rest frame. o But once the object starts moving, in the moving frame; the density will be, = m 1 1 V 1 Where is1the relativistic density,m is 1he relativistic mass and V 1 is the volume in moving frame. Step 2 of 3: Since when the object starts moving with higher speed, the mass of the object changes. That is given by m = m0 = m …………...1 1 1v 0 c Similarly when the object is moving in one direction, the volume is given by V = V 1 v2 = V 0………..2 1 0 c2 Using equation 1 and 2 in above equation of relativistic density, m0 1= V0 = m 02 1 V 0