Spherical particles of pollen are shaken up in water and allowed to settle. The depth of water is `2xx10^(-2)m`. What is the diameter of the largest particles remaining in suspension one hour later?
Density of pollen `=1.8xx10^(3)kgm^(-3)` viscosity of water `=1xx10^(-2)` poise and density of water `=1xx10^(3)kgm^(-3)`

Explanation

Terminal velocity of the spherical of pollen, falling through water is
`upsilon=(2 (rho -rho_(0))gr^(2))/(9 eta)` ..(i)
The paricle will not be reaching the bottom in a time t if
`upsilon le d/t = (2 xx 10^(-2)m)/(1 hour) = (2 xx 10^(-2)M)/(60 xx 60s) = (10^(-4))/(18) ms^(-1)`
from (i), ` r = [(9 eta upsilon)/(2(rho - rho_(0))g)]^(1//2)`
`=[(9 xx 10^(-2) xx (10^(-4)//18))/(2[(1.8 xx 10^(3)-1 xx 10^(3))xx9.8])]^(1//2)`
`=5.6 xx 10^(-6)m`.