QUESTION $1[25$ MARKS$]$

a$)$ Figure $1($a$)$ shows a velodrome, an arena for track cycling. Figure $1($b$)$ is the crosssectional area of the cycling track. Determine the centroid of the shaded area.

$[12$ Marks$]$

$($a$)$

$($b$)$

Figure $1$: $($a$)$ Velodrome and $($b$)$ partial cross$-$sectional area of the velodrome.

b$)$ Figure $2$ shows a signboard that is attached with a cable at A and a pin at C $.$ Determine the coordinate of the center of gravity of the signboard.

$[13$ Marks$]$