A flat pie shaped wedge cut from a disc lies in the XOY plane. The disc has radius a. The angle of the wedge is 2θ. The density of the disc is rho = rho0r = rho0 p x 2 + y 2 , where r is the distance of the point (x, y) from O. 1. Find the moment of inertia of the wedge about the z-axis. 2. Find rg the distance of the center of gravity of the wedge from O. 3. The z-axis is rotated till it is horizontal. The wedge is allowed to oscillate freely about O in the vertical xOy plane. What is the period of small oscillations?