  We study the effects of shear and density inhomogeneities in the formation of
naked singularities in spherically symmetric dust space--times. We find that in
general neither of these physical features alone uniquely specifies the end
state of the gravitational collapse. We do this by (i) showing that, for open
sets of initial data, the same initial shear (or initial density contrast) can
give rise to both naked and covered solutions. In particular this can happen
for zero initial shear or zero initial density contrast; (ii) demonstrating
that both shear and density contrast are invariant under a one parameter set of
linear transformations acting on the initial data set and (iii) showing that
asymptotically (near the singularities) one cannot in general establish a
direct relationship between the rate of change of shear (or density contrast)
and the nature of the singularities. However, one can uniquely determine the
nature of the singularity if both the initial shear and initial density
contrast are known.
  These results are important in understanding the effects of the initial
physical state and in particular the role of shear, in determiming the end
state of the gravitational collapse.
