Figure $5$

As shown in Figure $5,$ a pendulum consists of two solid cylindrical rods $\backslash ($ A B $\backslash )$ and $\backslash ($ O C $\backslash )$ which have a linear mass of $\backslash (3\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}\backslash ).$ A washer of mass $\backslash (12\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash )$ and uniform thickness, centred at $\backslash ($ D $\backslash ),$ is then attached to the longer rod at $\backslash ($ C $\backslash ).$

$($a$)$ Determine the total mass of the pendulum.

$($b$)$ Determine the location $\backslash ($ y $\backslash )$ of the centre of mass $\backslash ($ G $\backslash )$ of the pendulum.

$($c$)$ Calculate the moment of inertia of the pendulum about an axis perpendicular to the page and passing through $\backslash ($ G $\backslash ).$