Two uniform spheres shown in figure can rotate separately on parallel axis. The upper sphere has angular speed ω₀ and lower sphere is at rest. Now the two spheres are moved together so that their surfaces touch. After a short time the two spheres now in contact are rotating without slipping. Find the final rate of rotation of upper sphere in rad/s. [given moment of inertia of upper sphere I₁ = 4 kg m², moment of inertia of lower sphere I₂ = 2 kg m², a = 2 m, b = 1 m, ω₀ = 12 rad/s].