A uniform rod of length L rests on a frictionless horizontal surface. The rod pivots about a fixed frictionless axis at one end. The rod is initially at rest. A bullet traveling parallel to the horizontal surface and perpendicular to the rod with speed v strikes the rod at its center and becomes embedded in it. The mass of the bullet is one-fourth the mass of the rod.
(a) What is the final angular speed of the rod?
(b) What is the ratio of the kinetic energy of the system after the collision to the kinetic energy of the bullet before the collision?