4. A point-like bug of mass m lies on the rim of a uniform disk of mass M that can rotate freely about its center. Initially the bug and disk rotate together with an angular velocity ω₀. Then the bug walks half way to the center of the disk. What is ratio of the new kinetic energy of the system to its initial kinetic energy? (A) (4m+2M)/(m+2M) (B) (m+2M)/(4m+2M) (C) (2m+4M)/(2m+M) (D) (2m+M)/(2m+4M)