Question $2)$ Determining the particle relative density, specific volume and unit weight

from experimental results

a$)2kg$ of dry sand is poured into a Eureka can, where it displaces $755c{m}^3$ of water.

Calculate the relative density $($specific gravity$)$ of the sand particles.

b$)$ When $2kg$ of the same sand is poured into a measuring cylinder of diameter $6cm,$ it

occupies a total volume of $1200c{m}^3.$ Calculate the specific volume of the sand and its

unit weight in this state.

c$)$ The measuring cylinder is carefully filled with water up to the level of the top of the

sand, so that the total volume is still $1200c{m}^3.$ Calculate the unit weight of the saturated

sand in this condition.

d$)$ The side of the measuring cylinder is tapped gently several times, and the level of the

sand surface settles to an indicated volume of $1130c{m}^3.$ Calculate the specific volume

and the unit weight of the saturated sand in its dense state.

Take the unit weight of water ${}_{}$ as $9\mathrm{.}81k\frac{N}{m^3},$ and the mass density of water as $1000k\frac{g}{m^3}.$