Question $6(15$ Marks, CLO: $6)$ Dynamic$)$

The pendulum consists of a plate having a weight of $12$ N and a slender rod having a weight of $4$ N $.$ Point O is fixed as shown in the figure.

The plate is $0\mathrm{.}1$ m by $0\mathrm{.}1$ m and the length of the rod is $0\mathrm{.}5$ m $.$

Part $1.$ Determine the mass of the plate and the mass of the rod.

Part $2.$ Determine the pendulum's mass moment of inertia about an axis perpendicular to the page and passing through point O $.$

Part $3.$ Determine the radius of gyration of the pendulum about an axis perpendicular to the page and passing through point O $.$