The linear density of a thin rod is given by $=$ cx$2,$ where c is a constant and x is

the distance measured from one end. The rod is of length b$.$ Use a coordinate system

where the origin is at the $$light$($ $=0)$ end of the rod and in which the x$-$axis is

along the direction of the rod. Find

$($a$)$ the centre of mass of the rod and

$($b$)$ the moment of inertia about an axis passing through the origin and perpendicular

to the rod. Remember that the moment of inertia must be written in terms of

the mass, m$,$ of the rod.