  In this paper, we study the dynamical instability of gaseous sphere under
radial oscillations approaching the Reissner-Nordstr\"om limit. For this
purpose, we derive linearized perturbed equation of motion following the
Eulerian and Lagrangian approaches. We formulate perturbed pressure in terms of
adiabatic index by employing the conservation of baryon numbers. A variational
principle is established to evaluate characteristic frequencies of oscillations
which lead to the criteria for dynamical stability. The dynamical instability
of homogeneous sphere as well as relativistic polytropes with different values
of charge in Newtonian and post-Newtonian regimes is explored. We also find
their radii of instability in terms of the Reissner-Nordstrom radius. We
conclude that dynamical instability occurs if the gaseous sphere contracts to
the Reissner-Nordst\"orm radius for different values of charge.
