On the virtual mass of a rough sphere

Within the framework of the model of granular roughness formed by a large number of small grains distributed over the surface of a sphere, the accelerated combined motion of the sphere and the spherical grains attached to its surface in a resting ideal fluid is considered. Using the self-consistent field method, an expression is obtained for the virtual mass of the rough sphere as a function of the size of the grains and their distribution over the sphere surface. For a statistically uniform distribution of the grains over the sphere surface, the dependence of the mean value of the virtual mass of the rough sphere on the grain size is determined in the first approximation in their volume fraction.