## College Physics (4th Edition)

We can rank the spheres in order of decreasing viscous drag force: $d = e \gt b = c \gt a$
We can write an expression for the viscous drag force for a falling sphere: $F_D = 6\pi~\eta~rv$ We can find an expression for the viscous drag force in each case. (a) $F_D = 6\pi~\eta~rv$ $F_D = (6\pi~\eta)~(1.0~mm)(15~mm/s)$ $F_D = (6\pi~\eta) \times (15~mm^2/s)$ (b) $F_D = 6\pi~\eta~rv$ $F_D = (6\pi~\eta)~(1.0~mm)(30~mm/s)$ $F_D = (6\pi~\eta) \times (30~mm^2/s)$ (c) $F_D = 6\pi~\eta~rv$ $F_D = (6\pi~\eta)~(2.0~mm)(15~mm/s)$ $F_D = (6\pi~\eta) \times (30~mm^2/s)$ (d) $F_D = 6\pi~\eta~rv$ $F_D = (6\pi~\eta)~(2.0~mm)(30~mm/s)$ $F_D = (6\pi~\eta) \times (60~mm^2/s)$ (e) $F_D = 6\pi~\eta~rv$ $F_D = (6\pi~\eta)~(3.0~mm)(20~mm/s)$ $F_D = (6\pi~\eta) \times (60~mm^2/s)$ We can rank the spheres in order of decreasing viscous drag force: $d = e \gt b = c \gt a$