  We have analysed the NA50 data, on the centrality dependence of $p_T$
broadening of $J/\psi$'s, in Pb+Pb collisions, at the CERN-SPS. The data were
analysed in a QCD based model, where $J/\psi$'s are suppressed in 'nuclear'
medium. Without any free parameter, the model could explain the NA50 $p_T$
broadening data. The data were also analysed in a QGP based threshold model,
where $J/\psi$ suppression is 100% above a critical density. The QGP based
model could not explain the NA50 $p_T$ broadening data. We have also predicted
the centrality dependence of $J/\psi$ suppression and $p_T$ broadening at RHIC
energy. Both the models, the QGP based threshold model and the QCD based
nuclear absorption model, predict $p_T$ broadening very close to each other.
