Mass Distribution & Center of Mass: Why Does 1/r^3 Not Work?

[M-Speezy]

For center of mass problems, it's possible to use a variable mass distribution. For a half cylinder, I've been looking at different mass distributions (constant, 1/r, 1/r^2, etc.) My teacher pointed out that at some point it runs into problems. I found that this was the case at 1/r^3, as you evaluate ln(r) from 0 to R, which gives infinite mass. Could someone please provide a physical explanation as to why this is so different from 1/r^2? (Which gives half the diameter times the charge density magnitude, by the way).

Thanks.

 

[Simon Bridge]

You did the maths - didn't you notice the difference during the calculation?
Your teacher pointed out that "it" runs into problems... what is "it"?

 

[Jonnyb42]

The math shows the theoretical distributions of mass, not necessary to be physically possible for any power of 1/r. So it's really a matter of discussing what actual densities are possible. You also asked to give a physical explanation to a seemingly math confusion, so you may want to specify what your asking.