A cubical block with length $\backslash ($ L $\backslash )$ is floating in water. At equilibrium, a fraction $\backslash ($ f $\backslash )$ of the block is submerged under the water. The density of water is $\backslash (\backslash$rho$\_\{$w$\}\backslash ).$

Equilibrium position

Displaced position

$($i$)$ What is the average density of the block? Express the answer in terms of $\backslash ($ f $\backslash )$ and $\backslash (\backslash$rho$\_\{$w$\}\backslash ).(3$ pts$)$

$($ii$)$ If the block is displaced vertically from the equilibrium position by a distance $\backslash ($ x $\backslash ),$ with $\backslash ($ x $\backslash$ll$(1-$f$)$ L