HW Problem 41

Because the system is already in an eigenstate with eigenvalue 0, the value is already determined and therefore the uncertainty is 0. The question states that the spherical harmonic $Y_{0,0}$ is an eigenfunction of $L_{zop}$, and therefore the components of angular momentum for $l_{x,y,z}$ are all 0. This is consistent with the uncertainty relationship because $0\times 0=0$.