The constraints are examined which may be obtained for the parameters of long-range hypothetical interactions by the use of the precise experimental setup created originally for the calibration of accelerometers. This setup includes the large rotating steel sphere with a nonconcentric spherical cavity in which the strictly homogeneous gravitational field arises. The field of additional interaction produced by the atoms of the sphere, however, is not homogeneous. The essential features required of the detector of additional interaction which is the torsional pendulum of high sensitivity are discussed. Both the cases of the Yukawa-type and degree-type hypothetical interactions are investigated. It is shown that the known-to-date constraints for Yukawa-type interactions may be strengthened by a factor of 400 in the appropriate interaction range. For the degree-type hypothetical forces decreasing with distance as r-3, r-4 and r-5 correspondingly the known constraints may be strengthened by the factors of 90, 35 and 20. The conclusion is made that with the use of the specially created related setup it will be conceivable to strengthen the constraints for Yukawa-type interactions up to 4500 times over a wide interaction range.