  We show that violation of variance based local sum uncertainty relation
(LSUR) for angular momentum operators of a bipartite system, proposed by
Hofmann and Takeuchi, Phys. Rev. A 68, 032103 (2003)], is necessary and
sufficient for entanglement in two-qubit permutation symmetric state. Moreover,
we also establish its one-to-one connection with negativity of covariance
matrix [Phys. Lett. A 364, 203 (2007)] of the two-qubit reduced system of a
permutation symmetric N-qubit state. Consequently, it is seen that the
violation of the angular momentum LSUR serves as a necessary condition for
pairwise entanglement in $N$-qubit system, obeying exchange symmetry. We
illustrate physical examples of entangled permutation symmetric N-qubit
systems, where violation of the local sum uncertainty relation manifests itself
as a signature of pairwise entanglement.
