  We investigate here the locally naked singularity formed due to a spherically
symmetric inhomogeneous collapsing cloud having non-zero isotropic pressure, in
terms of its strength. Sufficient condition provided by Clarke and Krolak for
it to be Tipler strong has been used to restrict the parameters that represent
the non-linear relation between the physical radius and the radial coordinate
of the outgoing radial null geodesic at the singular center. Studying end state
of a collapsing cloud requires information about the dynamics of collapse,
which is unknown in a general scenario. Hence we study small perturbations to
the mass profile for inhomogeneous dust, which is possible using the formalism
developed here. This perturbed mass profile, in turn, gives rise to non-zero
pressure. We show the existence of a non-zero measure set of initial data
giving rise to such strong curvature naked singularity.
