Two (spherical) species are to be separated by centrifugation. the ratio between the rrodified mass and the viscous coefficient (6par) is 3.1 x 10" s for the second species, and 4.9 x 10-3 s for the first species. the diffusion coefficients are, respectively, 1.1 x 10"0 and 8.7 x 10" m'/s. a) determine the minimum length of the tube that should be used to allow for a successful separation considering the (apparent) centrifugal acceleration to be 8 x 10g. b) what would be the consequence(s) of using a longer tube?

Consider a uniformly charged ring in the xy plane, centered at the origin. the ring has radius a and positive charge qdistributed evenly along its circumference. a)what is the direction of the electric field at any point on the z axis? . b)what is the magnitude of the electric field along the positive z axis? use k in your answer, where k=14πϵ0. d)the ball will oscillate along the z axis between z=d and z=−d in simple harmonic motion. what will be the angular frequency ω of these oscillations? use the approximation d≪a to simplify your calculation; that is, assume that d2+a2≈a2. express your answer in terms of given charges, dimensions, and constants