$3\mathrm{.}12$ A sector$-$shaped sluice gate having a radius of cur$-$

vature of $5\mathrm{.}4$ m is as shown in Fig $3\mathrm{.}27.$ The centre of

curvature $C$ is $0\mathrm{.}9$ m vertically below the lower edge $A$ of the

gate and $0\mathrm{.}6$ m vertically above the horizontal axis passing

through O about which the gate is constructed to turn. The

mass of the gate is $3000$ kg per metre run and its centre of

gravity is $3\mathrm{.}6$ m horizontally from the centre O $.$ If the water

level is $2\mathrm{.}4$ m above the lower edge of the gate, find per metre

run $($a$)$ the resultant force acting on the axis at O $,($b$)$ the

resultant moment about O $.$

FIGURE $3\mathrm{.}27$

$[($a$)39\mathrm{.}2$ kN$,($b$)106$ kNm