Proposal for an experiment to search for Randall-Sundrum-type corrections to Newton’s law of gravitation

String theory, as well as the string inspired brane-world models such as the Randall-Sundrum (RS) one, suggest a modification of Newton’s law of gravitation at small distance scales. Search for modifications of standard gravity is an active field of research in this context. It is well known that short range corrections to gravity would violate the Newton-Birkhoff theorem. Based on calculations of RS-type non-Newtonian forces for finite size spherical bodies, we propose a torsion balance based experiment to search for the effects of violation of this theorem valid in Newtonian gravity as well as in the general theory of relativity. We explain the main principle behind the experiment and provide detailed calculations suggesting optimum values of the parameters of the experiment. The projected sensitivity is sufficient to probe the RS parameter up to 10 microns.