Q$2$

A $1$ m diameter cylindrical mass, $\backslash ($ M $\backslash ),$ is connected to a $2$ m wide rectangular gate as shown in figure $2.$ The gate is required to open when the water level, $\backslash ($ h $\backslash ),$ drops below $2\mathrm{.}5$ m $.$

Figure $2$: The mass will open the gate when the depth of the water drops below $2\mathrm{.}5$ m $.$

a$.$ Draw a free body diagram of the forces acting on the mass

b$.$ What is the resultant force $\backslash (\backslash$mathrm$\{$F$\}\_\{\backslash$mathrm$\{$R$\}\}\backslash )$ experienced by the gate when $\backslash (\backslash$mathrm$\{$h$\}=2\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash )$ and where does it occur? $(8$ marks$)$

c$.$ Determine the required value for M to open the gate. Neglect friction at the gate hinge and the pulley. $(10$ marks$)$

d$.$ Briefly explain using diagrams the Archimedes principle.

$($Total: $25$ marks$)$