Problem $1$: A liquid limit test has been performed on a soil using the Casagrande cup. In this

test, exactly $25$ drops of the cup were required to close the bottom of the standard groove

along a longitudinal distance of $\frac{1}{2}$ in$.$ A moisture content test was then performed on

the tested soil and yielded the following results:

Mass of soil $+$ can before placing in oven $52\mathrm{.}20$ g

Mass of soil $+$ can after removal from oven $41\mathrm{.}52$ g

Mass of can $22\mathrm{.}40$ g

Based on this test only, compute the liquid limit of the soil.