$2$ a$)$ In a hydrometer test, $48g$ of soil passing $75$ sieve is dispersed in $1000cc$ jar of water. In order to find the percent finer than $0\mathrm{.}003mm$ particle size, how long the test is to be continued? The centre of hydrometer bulb is $165mm$ below the surface of water. Take the viscosity of water as $1{10}^{-5}g-s\frac{ec}{c{m}^2}$ and $G=2\mathrm{.}72.$ If the hydrometer reading corresponding to this time is $1\mathrm{.}011,$ what is the percent finer than $0\mathrm{.}003mm$ particle size?

$(5)$