$($a$)$ In a compaction test a bulk unit weight of $16$ kN$/$m

$3$ was measured at a moisture

content of $8\%.$ What would the moisture content have been if the soil had been fully

saturated. Assume Gs $=2\mathrm{.}70.$

$($b$)$ The mass of an oven$-$dried sample of clay is $11\mathrm{.}26$ gm and its volume is $5\mathrm{.}83$ cm$3.$

If the specific gravity of the soil particles is $2\mathrm{.}67$ determine the shrinkage limit of the

soil. The shrinkage limit is the moisture content the soil would have had if fully

saturated at its minimum volume.