Adilute solution of macromolecules (e. g., dna, proteins) at temperature t is placed in an ultracentrifuge that rotates with angular frequency ω. the centripetal acceleration ω 2 r acting on a particle of mass m may then be replaced by an equivalent centrifugal force mω2 r in the rotating frame of reference. (a) find how the relative density n(r) of molecules varies with their radial distance r from the axis of rotation.
(b) show quantitatively how the molecular weight of the macromolecules can be determined if the molecular density ratio n1/n2 at the radii r1 and r2 is measured by optical means.