A pendulum is composed of a thin uniform rod of length _ =1.9 m and mass 50 kg and a sphere with a cavity. Attached to the rod at the bottom is a sphere within a sphere. The outer blue-coloured sphere has volume density density p1 =3 kg/m^3. Inside the blue-coloured sphere is an inner sphere with volume density po =4.4 kg/m^3. The radius of the cavity is 72 =0.1 m and the radius of the outer sphere is 71 =0.4 m. Below is a cross-section of the pendulum. Take point P to be the origin and the pivot point of the pendulum. The pendulum swings in the plane of the page. Take the positive x and y directions to point to the right and down, respectively. The image below shows a cross-section of the pendulum. Hint: Think about how you can use positive and negative masses to derive the moment of inertia for the outer sphere. L P1 11 12 P2 a) Where is the centre of mass located? Icm = Number m yom = Number m b) What is the moment of inertia about point P? Ip Number kg. m2