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.