Answer
We can rank the spheres in order of decreasing viscous drag force:
$d = e \gt b = c \gt a$
Work Step by Step
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:
$d = e \gt b = c \gt a$
