suppose I have a 10 kg sphere with homogenous distribution of mass (aka density is same everywhere) that is 10 m^3. Now suppose I rapidly increased its radius at a speed of 1/2c m^3 (and because its homogenous the volume increased correspondingly). Now my question is whether that would cause the "relativistic mass" of the box to increase. Clearly some particles are moving at high velocity while one in the middle is stationary. Would it be possible to treat this entire system as opposed to each individual particle of mass?