USAAAO — 2023 First Round

Consider Galaxies A and B, both of which have radius R. At a distance R from its center, Galaxy A's rotational velocity is equal to v. Meanwhile, Galaxy B's radial velocity dispersion is also equal to v. However, galaxy A is spiral while galaxy B is spherical elliptical and composed of uniform, evenly-spaced stars. Calculate the masses of both galaxies. (Answer choices are listed as m_A; m_B).