Binding energy of a truncated singular isothermal sphere ($W=-G{M}_0^2/r_0$)

For $\rho =k/(2\pi G{r}^2)$ truncated at $r_0$, the enclosed mass is $M(r)=2kr/G$. The shell-assembly integral gives $W=-\int GM(r)dM/r=-G{M}_0^2/r_0$. The origin has divergent density but finite total mass and binding energy.