Question

Consider two spherical stones with same density (mass per unit volume). The larger stone has radius R = 8.58 cm and the smaller stone has radius r = 3.37 cm. Find the ratio of the terminal speed in air of the larger stone to that of the smaller stone.

Answer 1

weight = k r^3
drag = c r^2 v^2

at terminal speed, drag/weight = 1
drag/weight = const v^2/r

so
V1^2/R1 = V2^2/R2

V2^2/V1^2 = R2/R1

V2/V1 = sqrt (R2/R1)