  We study the physics of $\nu=1/2$ bosonic fractional quantum Hall droplets
confined in a ring-shaped region delimited by two concentric cylindrically
symmetric hard-wall potentials. Trial wave functions based on an extension of
the Jack polynomial formalism including two different chiral edges are proposed
and validated for a wide range of confinement potentials in terms of their
excellent overlap with the eigenstates numerically found by exact
diagonalization. In the presence of a single repulsive potential centered in
the origin, a recursive structure in the many-body spectra and a massively
degenerate ground state manifold are found. The addition of a second hard-wall
potential confining the fractional quantum Hall droplet from the outside leads
to a non-degenerate ground state containing a well defined number of quasiholes
at the center and, for suitable potential parameters, to a clear organization
of the excitations on the two edges. The utility of this ring-shaped
configuration in view of theoretical and experimental studies of subtle aspects
of fractional quantum Hall physics is outlined.
