  It is shown that a QCD based nuclear absorption model, with few parameters
fixed to reproduce experimental $J/\psi$ yield in 200 GeV pp/pA and 450 GeV pA
collisions can explain the preliminary PHENIX data on the centrality dependence
of $J/\psi$ suppression in Cu+Cu collisions at RHIC energy, $\sqrt{s_{NN}}$=200
GeV. However, the model does not give satisfactory description to the
preliminary PHENIX data on the centrality dependence of $J/\psi$ suppression in
Au+Au collisions. The analysis suggest that in Au+Au collisions, $J/\psi$ are
suppressed in a medium unlike the medium produced in SPS energy nuclear
collisions or in RHIC energy Cu+Cu collisions.
