  We analyze the influence of extra dimensions on the static equilibrium
configurations and stability against radial perturbations. For this purpose, we
solve stellar structure equations and radial perturbation equations, both
modified for a $d$-dimensional spacetime ($d\geq4$) considering that spacetime
outside the object is described by a Schwarzschild-Tangherlini metric. These
equations are integrated considering a MIT bag model equation of state extended
for $d\geq4$. We show that the spacetime dimension influences both the
structure and stability of compact objects. For an interval of central energy
densities $\rho_{cd}\,G_d$ and total masses $MG_d/(d-3)$, we show that the
stars gain more stability when the dimension is increased. In addition, the
maximum value of $M{G_d}/(d-3)$ and the zero eigenfrequency of oscillation are
found with the same value of $\rho_{cd}\,G_d$; i.e., the peak value of
$M{G_d}/(d-3)$ marks the onset of instability. This indicates that the
necessary and sufficient conditions to recognize regions constructed by stable
and unstable equilibrium configurations against radial perturbations are,
respectively, $dM/d\rho_{cd}>0$ and $dM/d\rho_{cd}<0$. We obtain that some
physical parameter of the compact object in a $d$-dimensional spacetime, such
as the radius and the mass, depend of the normalization. Finally, within the
Newtonian framework, the results show that compact objects with adiabatic index
$\Gamma_1\geq2(d-2)/(d-1)$ are stable against small radial perturbations.
