Question $1(20$ marks$)$:

The unit weight of a soil sample in natural conditions is $19\mathrm{.}1k\frac{N}{m^3}$ and its saturated unit

weight is $20\mathrm{.}1k\frac{N}{m^3}.$ Assuming a specific gravity of solids of $2\mathrm{.}5,$ calculate the following

properties of the soil in its natural conditions:

a$)$ void ratio,

b$)$ porosity,

c$)$ degree of saturation,

d$)$ moisture content, and

e$)$ buoyant unit weight.