  We investigate Kaluza-Klein models in the case of spherical compactification
of the internal space with an arbitrary number of dimensions. The gravitating
source has the dust-like equation of state in the external/our space and an
arbitrary equation of state (with the parameter $\Omega$) in the internal
space. We get the perturbed (up to $O(1/c^2)$) metric coefficients. For the
external space, these coefficients consist of two parts: the standard general
relativity expressions plus the admixture of the Yukawa interaction. This
admixture takes place only for some certain condition which is equivalent to
the condition for the internal space stabilization. We demonstrate that the
mass of the Yukawa interaction is defined by the mass of the
gravexciton/radion. In the Solar system, the Yukawa mass is big enough for
dropping the admixture of this interaction and getting good agreement with the
gravitational tests for any value of $\Omega$. However, the gravitating body
acquires the effective relativistic pressure in the external space which
vanishes only in the case of tension $\Omega=-1/2$ in the internal space.
