An earring is constructed from a thin ring and a uniform thin disk, rigidly attached at their edges. The earring swings frictionlessly from a pin that passes through the edge of the ring at the position opposite to the connection point with the disk. The disk has a mass that is 2.002 times the mass of the ring. The moment of inertia of the earring about the pin is 15 2 . The connection point between the disk and the ring suddenly fails and the disk falls off, leaving only the ring behind. Find the moment of inertia of the ring (in units of 2 ) that remains about the same pin. [leave at least three decimal places]