  We investigate the occurrence and nature of naked singularity for the
inhomogeneous gravitational collapse of Tolman-Bondi dust clouds.It is shown
that the naked singularities form at the center of the collapsing cloud in a
wide class of collapse models which includes the earlier cases considered by
Eardley and Smarr and Christodoulou. This class also contains self-similar as
well as non-self-similar models. The structure and strength of this singularity
is examined and the question is investigated as to when a non-zero measure set
of non-spacelike trajectories could be emitted from the singularity as opposed
to isolated trajectories coming out. It is seen that the weak energy condition
and positivity of energy density ensures that the families of non-spacelike
trajectories come out of the singularity. The curvature strength of the naked
singularity is examined which provides an important test for its physical
significance and powerful curvature growth near the naked singularity is
pointed out for several subclasses considered. The conditions are discussed for
the naked singularity to be globally naked. Implications for the basic issue of
the final fate of gravitational collapse are considered once the
inhomogeneities in the matter distribution are taken into account. It is argued
that a physical formulation for the cosmic censorship may be evolved which
avoids the features above. Possibilities in this direction are discussed while
indicating that the analysis presented here should be useful for any possible
rigorous formulation of the cosmic censorship hypothesis.
