Q$3$: A spherical glass particle is allowed to settle freely in water. If the particle starts initially

from rest and if the value of the Reynolds number with respect to the particle is $0\mathrm{.}1$ when

it has attained its terminal falling velocity, calculate:

$($a$)$ the distance travelled before the particle reaches $90$ per cent of its terminal falling

velocity,

$($b$)$ the time elapsed when the acceleration of the particle is one hundredth of its initial

value.

Q$4$: Calculate the distance a spherical particle of lead shot of diameter $0\mathrm{.}1mm$ settles in a

glycerol$/$water mixture before it reaches $99$ per cent of its terminal falling velocity. The density

of lead is $11,400k\frac{g}{m}3$ and the density of liquid is $1000k\frac{g}{m}3.$ The viscosity of liquid is $10$

$mN\frac{s}{m}2.$ It may be assumed that the resistance force may be calculated from Stokes' Law andis

equal to $3du,$ where $u$ is the velocity of the particle relative to the liquid.